Fiscal Policy and the Real Exchange Rate

Transcription

1 WP/12/52 Fiscal Policy and the Real Exchange Rate Santanu Chatterjee and Azer Mursagulov

2 2012 International Monetary Fund WP/12/52 IMF Working Paer Fiscal Policy and the Real Exchange Rate Preared by Santanu Chatterjee and Azer Mursagulov Authorized for distribution by René Weber February 2012 This Working Paer should not be reorted as reresenting the views of the IMF. The views exressed in this Working Paer are those of the author(s) and do not necessarily reresent those of the IMF or IMF olicy. Working Paers describe research in rogress by the author(s) and are ublished to elicit comments and to further debate. Abstract Government sending on infrastructure has recently increased sharly in many emerging-market economies. This aer examines the mechanism through which ublic infrastructure sending affects the dynamics of the real exchange rate. Using a two-sector deendent oen economy model with intersectoral adjustment costs, we show that government sending generates a nonmonotonic U-shaed adjustment ath for the real exchange rate with shar intertemoral tradeoffs. The effect of government sending on the real exchange rate deends critically on (i) the comosition of ublic sending, (ii) the underlying financing olicy, (iii) the intensity of rivate caital in roduction, and (iv) the relative roductivity of ublic infrastructure. In deriving these results, the model also identifies conditions under which the redictions of the neoclassical oen economy model can be reconciled with emirical regularities, namely the intertemoral relationshi between government sending, rivate consumtion, and the real exchange rate. JEL Classification Numbers:F3, F4, H5 Keywords: Fiscal olicy, ublic investment, consumtion, real exchange rate, intersectoral adjustment costs Author s Address:schatt@uga.edu; amursagulov@imf.org

3 Contents Page 1. Introduction The Analytical Framework Resource allocation in the rivate sector The ublic sector Macroeconomic equilibrium Current account dynamics Numerical Analysis The benchmark equilibrium Fiscal olicy shocks Exchange rate dynamics: sensitivity to financing olicies The ersistence of the real exchange rate The short-run correlation between government sending and rivate consumtion Sensitivity Analysis Sectoral outut elasticity of ublic caital Elasticity of substitution in roduction Intersectoral adjustment costs Conclusions...24 Tables 1. Benchmark equilibrium Government sending shocks: Long-run effects Government sending and the real exchange rate Government sending and short-run consumtion...29 Figures 1. Government sending shocks Government sending and the real exchange rate: sensitivity to financing olicies Government sending, the ersistence of the real exchange rate, and the time horizon Government sending and consumtion: sensitivity to the sectoral elasticity of ublic caital Government sending and the real exchange rate: sensitivity to the sectoral elasticity of ublic caital Government sending and the real exchange rate: sensitivity to the elasticity of substitution in roduction Government sending and the real exchange rate: sensitivity to intersectoral adjustment costs...36 References

4 1 Introduction Emerging markets such as China, India, and Brazil have recently embarked on an ambitious exansion of government sending, mainly on ublic infrastructure such as roads, airorts, rail, ower suly, water, telecommunication networks, etc., as a means to sustain their high economic growth rates from the last two decades. In contrast, many OECD countries are currently working to reduce ublic sending to reign in government debt, although sending on infrastructure has remained a otential area of exansion. In an era of global economic integration, the dynamic e ects of these olicies on external rices and cometitiveness will be of critical imortance for both develoing and develoed countries. Understanding this relationshi in the context of a dynamic general equilibrium model is the central objective of this aer. The link between government sending and the real exchange rate has been the subject of a growing but inconclusive literature in international macroeconomics. Seci cally, the redictions of the theoretical literature on this issue are sharly at odds with corresonding emirical ndings, mainly in three areas: 1 (1) The rst issue concerns the e ect of a change in government sending on the real exchange rate, esecially in the short run. The theoretical literature, based redominantly on the neoclassical deendent economy model, tyically treats government sending as reresenting ublic consumtion, thereby iminging on the economy as a ure demand shock. Consequently, the real exchange rate is redicted to areciate in the short run in resonse to an increase in government sending. The long-run real exchange rate, on the other hand, remains una ected, being determined solely by suly-side factors such as sectoral roductivity. In the short run, an increase in government consumtion increases the demand for non-traded goods and their relative rice (the real exchange rate areciates). This e ect is o set over time by a gradual dereciation of the exchange rate to its initial level. By contrast, several recent emirical studies have documented that government sending actually generates a real dereciation of the exchange rate in the short run. 2 However, emirical studies seldom distinguish between government investment and consumtion, thereby roviding little understanding of why the stylized facts are at odds with theoretical redictions. Given that ublic consumtion and investment might iminge on resource allocation in dramatically di erent ways, it is not clear whether the comosition of government sending might 1 The theoretical literature has relied redominantly on the two-sector deendent oen economy model; rominent contributions include Obstfeld (1989), van Wincoo (1993), Brock and Turnovsky (1994), Brock (1996), and Morshed and Turnovsky (2004). The emirical link between scal olicy and real exchange rate uctuations have been examined, among others, by Obstfeld (1993), Asea and Mendoza (1994), Chowdhury (2004), Kim and Roubini (2008), Galstyan and Lane (2009), Caorale et al. (2011) and Ravn et al. (2011). 2 See Monacelli and Perotti (2006) and Ravn et al. (2011) for some recent examles. 3

5 be driving the discreancy between theory and facts. A recent contribution by Galstyan and Lane (2009) attemts to address this discreancy, but by limiting their focus only to the long-run steady-state, and thereby abstracting away from intertemoral issues, they are not able to resolve the controversy over the short-run and transitional e ects of government sending on the real exchange rate. (2) Second, a large emirical literature has documented the strong ersistence of real exchange rate uctuations, imlying very long eriods of adjustment following an underlying shock. Moreover, these deviations of the exchange rate from its equilibrium often follow non-linear trajectories. 3 In contrast, the redicted deviations of the exchange rate (from equilibrium) generated by theoretical models are very short-lived and monotonic, with imlausibly fast seeds of convergence. This discreancy may be otentially resolved by focusing on government sending on infrastructure, rather than consumtion. There are three key factors in this context that may exlain both ersistence and non-linearity in the adjustment of the real exchange rate: rst, since ublic infrastructure is accumulated gradually over time, the short run resource withdrawal e ects described above in (1) must be evaluated against the long-run e ects on rivate roductivity, thereby indicating an intertemoral relationshi between government sending and the real exchange rate. Second, it may be costly for investors to re-allocate rivate caital across sectors in resonse to the long-run roductivity bene ts of ublic investment. Third, the e ects of underlying taxation olicies that nance such sending must also be considered as a source of both non-linearity and ersistence. These asects of ublic olicy are largely ignored in the existing literature. Given the ersistence of real exchange rate movements observed in the data, these e ects may not be fully catured by limited time-series data or a steady-state analysis. (3) Finally, a contentious olicy issue in the literature relates to the short-run correlation between government sending and rivate consumtion. Theoretical models redict a shortrun negative correlation: by withdrawing resources from the rivate sector, government sending raises the marginal utility of wealth which, in turn, leads agents to increase labor suly and reduce the consumtion of all normal goods in the short run. By contrast, the emirical literature has documented a ositive correlation between ublic sending and rivate consumtion in the short run. 4 Again, focusing on government investment rather than consumtion may hel resolve the issue at hand. An increase in government sending which is allocated to the creation of infrastructure caital will raise the long-run roductivity of both rivate caital and labor. Private agents, anticiating this long-run increase in their 3 See Engel (1993, 1999), Knetter (1993), Froot and Rogo (1995), Taylor (1995), Edwards and Savastano (1999), and Cheung and Lai (2000) for some early contributions. For non-linearities in the adjustment ath of the real exchange rate, see Taylor et al. (2001). 4 See, for examle, Fatas and Mihov (2001), Blanchard and Perotti (2002), and Ravn et al. (2011). 4

6 returns from rivate investment and labor suly (thereby anticiating higher income in the long-run) can choose to increase their rate of rivate consumtion in the short run, by borrowing from their future (higher) exected income. In this aer, we examine the mechanism through which government sending, secifically on ublic infrastructure, and accomanying nancing olicies a ect the dynamics of the real exchange rate. In doing so, we also attemt to reconcile the neoclassical deendent economy model with observed emirical regularities. We emloy a two-sector oen economy model with government-rovided infrastructure caital (henceforth "ublic caital") augmenting the roductivity of rivate caital and labor in both the traded and non-traded sectors. 5 This asect of our model relates to Galstyan and Lane (2009), but with three key di erences. First, while they restrict their analysis to the steady-state, we conduct a full dynamic analysis that characterizes the intertemoral trade-o s in the adjustment of the real exchange rate to government sending shocks. Second, while Galstyan and Lane (2009) assume that all ublic investment iminges only on non-traded outut and is nanced by lumsum taxes, we focus on a full range of scal issues, such as the sectoral comosition of government investment and the e ects of distortionary taxes on sectoral income. We also arameterize our model to comare the e ects of government consumtion with investment. Third, we introduce intersectoral adjustment costs to generate the observed ersistence in the adjustment of the real exchange rate. Seci cally, we assume that it is costly for agents to transfer rivate caital from the non-traded to the traded sector for investment uroses. While Galstyan and Lane (2009) assume a costless transfer of caital across sectors, we follow Morshed and Turnovsky (2004) in introducing convex costs of transferring rivate caital across sectors, and this turns out to be a crucial source of non-monotonicity in the adjustment of the real exchange rate. In this context, we also examine the e ects of government sending in the form of an investment subsidy that reduces these intersectoral adjustment costs. 6 As we will show, the combination of a gradually accumulating stock of ublic caital and intersectoral adjustment costs enables us to identify lausible conditions under which the 5 There is a voluminous literature on the role of ublic caital in a ecting economic growth, starting with the work of Aschauer (1989) and Barro (1990). Imortant theoretical contributions include Glomm and Ravikumar (1994), Fisher and Turnovsky (1998), Rioja (2003), and Agenor and Aizenman (2007); see Agenor (2011) for a comrehensive review. Gramlich (1994) and Bom and Lithgart (2010) rovide reviews of the corresonding emirical literature. 6 Morshed and Turnovsky (2004) rovide several examles from ost-world War II Western Euroe to motivate the resence of intersectoral adjustment costs, such as the costly retro- tting of war-time industries to roduce consumer goods in the ost-war era. Further, many develoing countries adot industrial olicies that directly or indireclty subsidize rivate investment in their exort sectors. These include the creation of Secial Economic Zones (SEZ), subsidies for R&D, tax breaks, etc. We model the subsidy as an investment tax credit for transfering caital from the non-traded sector to the traded sector. The investment tax-credit has also been studied for the one-sector deendent economy model; see, for examle, Sen and Turnovsky (1990). 5

7 two-sector deendent oen economy model yields qualitative redictions that are consistent with stylized facts. 7 The analytical structure we emloy yields a fth-order non-linear dynamic system with three state and two jum variables and hence requires a numerical solution. We consider three tyes of government sending olicies: (i) an increase in ublic investment from traded outut, (ii) and increase in ublic investment from non-traded outut, and (iii) an investment subsidy that reduces the cost of transferring caital from the non-traded to the traded sector. We assume that these sending increases can be nanced by (i) a lumsum tax (or government debt), (ii) a distortionary tax on traded outut, or (iii) a distortionary tax on non-traded outut. qualitatively consistent with stylized facts: Our numerical exeriments reveals some interesting results that are (a) In the resence of a gradually accumulating stock of ublic caital and intersectoral adjustment costs, government sending generates a ersistent and non-monotonic U-shaed adjustment ath of the real exchange rate (following its instantaneous resonse), thereby generating shar intertemoral trade-o s. 8 The intuition for this result stems from the fact that an increase in government sending on infrastructure and its long-run roductivity bene ts increase the demand for rivate investment in the short run in both sectors. Since the transfer of rivate caital across sectors is a costly activity, the non-traded sector accumulates rivate caital faster than the traded sector to reduce intersectoral adjustment costs (which are determined by the out ow of resources from the non-traded sector er unit of installed caital in that sector). Consequently, the marginal roduct of rivate caital in the non-traded sector increases at a slower rate than the corresonding marginal roduct in the traded sector (due to diminishing returns), causing a real dereciation of the exchange rate in the short and medium term. (b) The instantaneous, transitional (the length and deth of the U-shaed adjustment), and steady-state (long-run) resonse of the real exchange rate to an increase in ublic investment deends critically on (i) the sectoral comosition of government sending on infrastructure (i.e., whether the sending increase iminges on traded or non-traded outut), 7 A recent contribution by Cerra et al.(2010) also examines the e ects of nancing ublic investment by foreign aid. However, they model the ow of ublic investment as being relevant for roduction rather than the accumulated stock of ublic caital, along with a costless transfer of caital across sectors. The distinction between the stock and ow seci cations turns out to be crucial for the redictions of the model. Chatterjee et al.(2003) and Chatterjee and Turnovsky (2007) also analyze the issue of infrastructure nancing by foreign aid, but in the context of one-sector, one-good models of the oen economy, which abstract away from issues related to the exchange rate. 8 Non-linearities in the adjustment ath of the real exchange rate have been the subject of focus in models with transaction costs in international arbitrage; see Taylor et al. (2001) for a review of this literature. We also derive a non-linear adjustment ath, albeit from a very di erent source (intersectoral adjustment costs and a gradually accumulating stock of ublic caital). 6

8 (ii) the underlying nancing olicy (lumsum tax or sectoral income tax), (iii) the sectoral intensity of rivate caital, and (iv) the sectoral outut elasticity of ublic caital. We also identify conditions under which a short-run dereciation of the real exchange rate is reversed into a net real areciation in the long-run (through the Balassa-Samuelson e ect). Given the ersistence of the U-shaed adjustment ath, we argue that emirical studies that document a long-run real dereciation of the exchange rate in resonse to an increase in government sending may be icking u only a transitional e ect. (c) The observed short-run ositive correlation between government sending and consumtion is generated when (i) ublic caital is more roductive in the traded sector and (ii) the increase in ublic investment is from non-traded outut. Further, an investment tax-credit (subsidy) also generates this ositive correlation. These results are derived in the absence of a home bias in consumtion and indicate that the observed ositive correlation between government sending and consumtion is not inconsistent with the neoclassical model. In summary, we characterize the structural conditions under which the qualitative redictions of the neoclassical oen economy model can be reconciled with stylized facts regarding the relationshi between government sending, rivate consumtion, and the dynamics of the real exchange rate. We also check the sensitivity of the adjustment ath of the real exchange rate to (a) the sectoral outut elasticity of ublic caital, (b) the elasticity of substitution in roduction, and (c) intersectoral adjustment costs. In a recent contribution, Ravn et al.(2011) develo an oen economy model with dee habit ersistence and imerfect cometition to exlain the short-run correlations between government sending, the real exchange rate, and rivate consumtion. We view our contribution as comlementary to theirs, but without sacri cing the deendent economy framework on which the large bulk of theory on this issue has been develoed. The rest of the aer is organized as follows. Section 2 develos a canonical two-sector deendent economy model with ublic caital and intersectoral adjustment costs, Section 3 resents the numerical calibration of the model and the olicy exeriments, Section 4 discusses the sensitivity analysis, and Section 5 concludes. 2 The Analytical Framework We consider a small oen economy with an in nitely-lived reresentative agent who maximizes utility from the consumtion of a traded good and a domestically roduced nontraded good. The agent accumulates wealth over time through an internationally traded bond and faces a erfect world caital market with an exogenous interest rate. There are two 7

9 roduction sectors in this economy, namely the traded goods sector and the non-traded goods sector: Each sector uses three factors of roduction: rivate caital, labor, and a governmentrovided stock of ublic caital (infrastructure). The stock of ublic caital reresents a non-excludable and non-rival ublic good that enhances the roductivity of rivate caital and labor in both roduction sectors through a sillover e ect. The government aroriates fractions of both traded and non-traded outut for ublic investment, and nances this sending using distortionary income taxes (levied on incomes in both sectors) as well as lumsum taxes (or debt). Finally, we will also assume that all rivate investment takes lace in the non-traded sector, but it is costly for the agent to transfer resources to the traded sector for the creation of rivate caital in that sector. The agent receives an investment tax credit (or subsidy) from the government that is targeted towards reducing these intersectoral adjustment costs. We treat the traded good as a numeraire, so that the relative rice of the non-traded good is the real exchange rate, with an increase denoting a real areciation and vice-versa. 2.1 Resource Allocation in the Private Sector The reresentative agent s intertemoral utility function is given by Z 1 subject to a ow budget constraint U = U (C T ; C N ) e t dt; U i > 0; U ii < 0; i = T; N (1) 0 _B = (1 T ) Y T + rb + [(1 N )Y N C N I N (1 s)(x; K N )] C T T L (2) where, C T and C N denote the consumtion of the traded and non-traded good, resectively. B denotes an internationally traded bond which earns an exogenous world interest rate, r. The agent roduces outut Y T in the traded-goods sector and Y N in the non-traded sector. I N reresents rivate investment in the non-traded sector and (:) is the intersectoral adjustment cost incurred by the agent to transfer resources for investment in the traded sector. The agent ays taxes on outut roduced in both sectors, with traded outut being taxed at the rate T and non-traded outut being taxed at the rate N : The agent also ays a lumsum tax, T L, and receives an investment subsidy s, targeted towards reducing the cost of converting non-traded outut to investment in the traded sector. Finally, the relative rice of the non-traded good, i.e., the real exchange rate, is denoted by. 8

10 The rate of accumulation of rivate caital in each sector is given by _K T = X _K N = I N (3a) (3b) where K T is the stock of rivate caital in the traded sector, K N is the corresonding stock in the non-traded sector, and X is the roortion of non-traded outut that is allocated to rivate investment in the traded sector. traded sector for investment is given by (X; K N ) = X where h is the adjustment cost arameter. 9 The cost of transferring non-traded outut to the 1 + h 2 X K N ; h 0 (4) The agent is endowed with one unit of time for work, which it uses to allocate labor suly to the two sectors. The labor market equilibrium condition is then given by L T + L N = 1 (5) where L T is the emloyment in the traded sector and L N is the corresonding measure in the non-traded sector. Production of nal goods in the traded and non-traded sectors uses a standard neoclassical technology and three factors: sectoral rivate caital and labor, and the aggregate stock of ublic caital, K G, rovided by the government: Y i = Y i (K i ; L i ; K G ) ; i = T; N (6) The stock of ublic caital generates services that are comlementary to the rivate factors in each sector, enhancing their roductivity along the transition ath and in the long run. The market-clearing condition in the non-traded sector is given by Y N = C N + I N + (X; K N ) + G N (7) where G N reresents the roortion of non-traded outut used by the government for ublic 9 Note that h = 0 reresents the standard Heckscher-Ohlin seci cation, where it is costless to transfer caital across sectors. On the other hand, when h! 1, the model converges to the seci c factors model, with caital being immobile across sectors. 9

11 investment. Private caital in the non-traded sector then evolves according to _K N = Y N C N (X; K N ) G N (7a) The agent chooses the rate of consumtion of the two goods, sectoral investment, and the allocation of labor to maximize (1), subject to (2), (3a) and (3b), given (4). The agent takes the government olicy variables and the stock of ublic caital as given, and at the beginning of the lanning horizon, is endowed with an initial stock of bonds and rivate caital, given by B(0), K T (0), and K N (0). The current-value Hamiltonian function is H = U (C T ; C N ) e t dt (8) i +e h(1 t T ) Y T + rb + f(1 N )Y N C N I N (1 s)(:)g C T T L _B h i h i +q1e 0 t X _K T + q2e 0 t I N _K N where is the shadow rice of wealth held in the traded bond, and q 0 1 and q 0 2 are the resective shadow rices for traded and non-traded rivate caital. The otimality conditions are U T (C T ; C N ) = U N (C T ; C N ) = = r ) = (8a) (8b) (8c) _ + (1 _q 1 q 1 + (1 = q0 2 = q 2 (8d) T )@Y T =@K T q 1 = r (8e) 2 = r (8f) N + (1 s) h N 2 K N q 1 = 1 + (1 s)h X K N (8g) (1 T T = (1 N N (8h) Lim Be t = Lim q 1K T e t = Lim K Ne t = 0 (8i) t!1 t!1 t!1 The rst-order conditions (8a) and (8b) equate the marginal utility of consumtion from each sector to the marginal utility of wealth, denominated in terms of the traded bond. (8c) is the standard no-arbitrage condition for a small oen economy facing a erfect world caital 10

12 market: the rate of time reference must equal the world interest rate. This restricts the shadow rice of wealth to be a constant over time, and therefore =. (8d) states that the real exchange rate is equal to the shadow rice of non-traded caital, denominated in terms of the traded bond. (8e) is the no-arbitrage condition for investment in the traded sector, equating its net after-tax return to the world interest rate. Here, the shadow rice of tradedsector rivate caital is exressed relative to that of the traded bond (q 1 = q1= 0 ). (8f) is the corresonding no-arbitrage condition for rivate investment in the non-traded sector, where from (8d), we note that the shadow rice of non-traded sector caital exressed in units of the traded bond is essentially the real exchange rate. (8h) states that the after-tax return to labor in each sector must be the same in equilibrium, and (8i) lists the transversality conditions for the three rivate assets. From (8a) and (8b), we can derive the olicy functions for sectoral consumtion: C i = C i ; ; i = T; N (9a) < > < 0; i = T; N An increase in the marginal utility of wealth reduces the consumtion of both traded and non-traded good, as the agent increases labor suly to o set for the increase in : A real areciation of the exchange rate makes the non-traded good more exensive relative to the traded good, causing the agent to allocate resources away from non-traded consumtion towards traded consumtion. 10 Further, taking note of (6), we can derive the olicy functions for sectoral labor suly from (8h): L i = L i (; K T ; K N ; K G ) ; i = T; N (9b) < T > < 0; sign = sign ( G A real areciation draws resources into the non-traded sector, reducing traded-sector emloyment. An increase in the stock of rivate caital in the traded sector raises the marginal roduct of labor in that sector, raising emloyment. Exactly the oosite haens when non-traded caital increases. Finally, the e ect of a higher stock of ublic caital on emloyment in the traded sector is ambiguous and deends on the relative roductivity of ublic caital in the traded sector,. If ublic caital is more roductive in the traded sector, 10 The details of these results are available on request from the authors. 11

13 emloyment in that sector increases, and vice versa. 11 To obtain the rate of rivate investment in the traded-goods sector, we di erentiate (8g) with resect to time, while taking note of (8e) and (8f): _X = YN C N G N + (1 N N K N K N (1 s)h 2.2 The Public Sector X (1 T T (1 s)(1 N N 1 + s 1 + h XKN X 2 2K N The government sends both traded and non-traded outut to generate new ublic investment in ublic caital. (i = T; N). The sending rules for each sector are (9c) Let sectoral sending by the government be given by G i G i = g i Y i ; 0 < g i < 1; i = T; N (10a) where g i reresents the rate of ublic investment from sector i (i = T; N). As such, g i reresent olicy variables for the government which can be used to alter the rate of sectoral rivate investment. These can also be thought of as reresenting the comosition of government sending on infrastructure. Public caital accumulates according to _K G = G T + G N G K G = g T Y T + g N Y N G K G (10b) where G reresents the rate of dereciation of ublic caital. 12 The government maintains a balanced budget at all oints of time, using tax revenues to nance sending on infrastructure and the investment subsidy: G T + [G N + s(x; K N )] = T Y T + N Y N + T L (11) The evolution of the current account is obtained by combining (2) with (11): _B = rb + (1 g T )Y T C T (12) 11 The details of these results are available on request from the authors. 12 Since this is a neoclassical model with a stationary steady-state, and the government is not an otimizing entity, we need a ositive rate of dereciation for ublic caital to close the model. Otherwise, sending on ublic investment would have to arbitrarily jum to zero at the steady-state, which could not be justi ed with a assive government. 12

14 2.3 Macroeconomic Equilibrium The core equilibrium dynamics are reresented by a fth-order non-linear di erential equation system with three state variables, K T ; K N ; and K G and two jum variables, and X : _K T = X _K N = Y N C N G N X 1 + h 2 X K N (13a) (13b) _K G = g T Y T + g N Y N G K G (13c) " _ = (1 N N (1 s) h # 2 X N 2 K N _X = YN C N G N + (1 N N K N K N (1 s)h X (1 T T (1 s)(1 N N 1 + s 1 + h XKN X 2 2K N (13e) The steady-state is attained when _K i = _ K G = _ X = _ = 0 (i = T; N) (14) At the steady-state equilibrium, the current account is given by ~Y T = C T (~; ) + g T ~ YT r ~ B (15) where the "~" denotes a steady-state quantity for an endogenous variable. To solve the model, we will assume that at the initial re-shock steady-state, the economy does not hold any debt or credit, i.e., ~ B0 = 0. This only alies to the initial equilibrium and will not hold once a shock is realized and absorbed by the economy, as will be shown in the next section. The steady-state condition (14), along with (15) (with ~ B = ~ B 0 = 0), (5) and (8h) yield 8 equations that can be solved for the steady-state quantities ~ K T ; ~ K N ; ~ K G ; ~ X; ~; ; ~ L T ; and ~ L N. Note also from (13a) that at the steady state, there is no new investment in rivate caital in the traded sector, i.e., ~ X = 0. The linearized dynamics around this initial steady-state can be exressed as _Z 0 = Z 0 0 Z ~ (16) 13

15 where Z 0 = (K T ; K N ; K G ; ; X) is the vector of state and controls, is a 5x5 matrix of linearized coe cients, and Z ~ 0 = ~KT ; K ~ N ; K ~ G ; ~; X ~ is a vector of steady-state quantities. The equilibrium dynamics are characterized by three stable (negative) eigenvalues, denoted by i (i = 1; 2; 3) and two unstable eigenvalues. 2.4 Current Account Dynamics In this section, we solve for the dynamics of the current account following a shock to the initial steady-state equilibrium in (13)-(15). 13 The otimal (linearized) time aths of the endogenous variables in the vector Z 0 takes the following canonical form: Z(t) ~ Z = A1 v j1 e 1 t + A 2 v j2 e 2 t + A 3 v j3 e 3 t ; j = 1; :::; 5; and Z = K T ; K N ; K G ; ; X (17) where A 1 ; A 2, and A 3 reresent the constants associated with the stable eigenvalues 1 ; 2 ; and 3 ; resectively, and v ji (i = 1; 2; 3) denote the normalized eigenvectors associated with each stable eigenvalue, where we aly the normalization v 1i = 1: Linearizing the current account equation in (12) around the steady-state equilibrium, we can derive the following (linearized) di erential equation for the current account: _B = r B B ~ + 1 K T KT ~ + 2 K N KN ~ + 3 K G KG ~ + 4 ( ~) (18) 1 = (1 g T ) T ; 2 T 3 G G ; 4 = N g T T with all the artial derivatives evaluated at the steady-state. Using (17) in (18), solving the resulting di erential equation, and imosing the transversality condition for the traded bond from (8i) leads to the following adjustment ath for the current account B(t) = ~ B + 3X i=1 i i r e i t (19) 13 The solution rocedure outlined in this section closely follows Turnovsky (1997) and is also similar to the one in Morshed and Turnovsky (2004). 14

16 where i = A i 4P j=1 jv ji ; i = 1; 2; 3: At t = 0, (19) gives B(0) = ~ B + 3X i=1 i i r (19a) Under the assumtion that B(0) = 0, (19a) can be solved for the steady-state level of the current account, ~ B following a shock. Once ~ B is known, then (19) comletely characterizes the evolution of the current account. 3 Numerical Analysis The analytical model described in section 2 is too comlex for a closed-form solution, and therefore must be evaluated numerically. To solve the model, we roose the following functional forms for the utility and roduction functions: Y T = A T K G Y N = A N K G U(C T ; C N ) = (C1 T CN ) ; 2 [0; 1]; 1 < < 1 (20a) K T + (1 )L 1 T ; A T > 0; ; 2 (0; 1); 2 ( 1; 1) (20b) 'K N 1 + (1 ')L N ; A N > 0; '; 2 (0; 1); 2 ( 1; 1) (20c) where is related to the intertemoral substitution in consumtion, e = 1=(1 is the relative imortance of non-traded consumtion in the agent s utility function. ) and overall roductivities of the traded and non-traded sectors are determined by an exogenous comonent given by A T and A N ; resectively, and the aggregate stock of ublic caital in the economy, rovided by the government. The arameters and denote the sectoral outut elasticities of ublic caital. Given the homogeneity of the roduction functions, and ' reresent the caital intensity in the traded and non-traded sectors, resectively, Finally, is related to the elasticity of substitution between rivate caital and labor in the roduction function by s = 1=(1 + ). familiar Cobb-Douglas roduction function. The The case where s = 1 ( = 0) aroximates the 3.1 The Benchmark Equilibrium Table 1A describes the arameterization of the benchmark economy. The reference arameter is chosen to yield an intertemoral elasticity of substitution in consumtion of 0:4, consistent with the evidence reviewed by Guevenen (2006). The choice of = 0:5 15

17 ensures that there is no home bias in consumtion and each good has the same weight in the utility function. The world interest rate is set at 6 ercent. The exogenous roductivity arameters A T and A N are chosen to yield a lausible benchmark equilibrium. The outut elasticity of ublic caital is set to 0:15 in each sector as a benchmark seci cation. There is a large emirical literature on the estimation of this elasticity and the range of estimates lie between 0:1 0:3; see Gramlich (1994). In a recent contribution, Bom and Lithgart (2009) review 67 such studies and estimate the long-run elasticity to be 0:146, which is close to our benchmark seci cation. We will, of course, conduct a sensitivity analysis by di erentially varying the sectoral elasticities. The intersectoral adjustment cost arameter is set at h = 30, following the calculations of Morshed and Turnovsky (2004). Again, this arameter will be subject to a sensitivity analysis. We assume a rate of ublic investment from traded outut, g T = 0:02 and from non-traded outut, g N = 0:07 to ensure that about 4:6% of aggregate outut is sent on infrastructure investment, which is also the long-run average for most OECD countries. Given this seci cation, about 21 ercent of government sending comes from the traded goods sector, while 79 ercent comes from the non-traded sector. We also assume that there are no distortionary taxes or subsidies in the benchmark equilibrium and all government sending is nanced through lumsum taxes. The benchmark equilibrium is calibrated for the Cobb-Douglas roduction function. Table 1B reorts the benchmark steady-state equilibrium for two cases: (i) the traded sector is more caital intensive than the non-traded sector ( = 0:35; ' = 0:25) and (ii) the non-traded sector is more caital intensive than the traded sector ( = 0:25; ' = 0:35). 14 For examle, in the case where the traded sector is more caital intensive, the caital-labor ratio in the traded and non-traded sectors are about 14:26 and 8:83, resectively. The caitaloutut ratio is 3:05 in the traded sector and 7:97 in the non-traded sector. The allocation of labor to the traded sector is 0:45 and the share of traded outut in GDP is about 0:49. The share of consumtion of each good in GDP is about 0:48 (since there is no home bias). The steady-state aggregate caital-outut ratio is 3:62 and the ratio of ublic to rivate caital is 0:25. The long-run real exchange rate is about 1: Fiscal Policy Shocks Table 2 reorts the long-run e ects of three scal olicy shocks on the macroeconomy and the resultant change in intertemoral welfare. in Table 1B to the following three government sending shocks: We subject the benchmark equilibrium 14 It is well known in the deendent oen economy models that the dynamics deend critically on the sectoral caital intensities; for a detailed discussion see Turnovsky (1997). 16

18 a. An increase in ublic investment from traded outut: g T increases ermanently from 0:02 to 0:05. b. An increase in ublic investment from non-traded outut: g N increases ermanently from 0:07 to 0:1. c. An increase in the investment subsidy to reduce intersectoral adjustment costs in the non-traded sector: s rises ermanently from 0 to 0:1. In olicy changes a and b, we calibrate the increase in government sending to ensure that in each case total government investment rises from its benchmark rate of 4:6 ercent to about 6 ercent of GDP. In all three cases, the sending increase is nanced by an aroriate adjustment of lumsum taxes to balance the government s budget. For the benchmark case, using a non-distortionary nancing instrument has the advantage of decouling the e ects of sending from revenues. The long-run imact of these scal shocks are reorted for two alternative scenarios: where the traded sector is more caital intensive and vice versa. The steady-state changes in variables are reorted relative to their re-shock benchmark levels, so that a value greater than one indicates an increase and vice versa. The e ect on welfare is reorted as a ercentage change. 15 As is evident from Table 2A and 2B, all three government sending shocks, being tied to investment activity, have an exansionary e ect on the economy in the long-run, with the caital-labor ratio increasing in both sectors, along with aggregate consumtion and GDP. The share of labor emloyment in the traded sector and traded outut in GDP increase in all three cases, indicating that the non-traded sector shrinks relative to the traded sector. Intertemoral welfare imroves when government sending is directed towards ublic investment. However, the investment subsidy generates a net welfare loss for the economy. also note that the investment subsidy is the least exansionary of the three scal sending shocks. The long-run change in the real exchange rate deserves some comment. For the cases where government sending increases ublic investment, the long-run real exchange rate areciates when the traded sector is more caital intensive. We By contrast, when the non-traded sector is more caital intensive, there is a long-run real dereciation. In the case of the investment subsidy, the real exchange rate areciates irresective of the sectoral caital intensity. The intuition behind the above results can be better understood by a deiction of the dynamic resonse of the economy to these shocks. This is illustrated in Figure 1, which lots the time aths of labor emloyment in the traded sector, the share of traded outut 15 Changes in welfare levels are comuted by an equivalent variation in outut across steady states, i.e., we determine the required change (in ercentage terms) in the initial outut level (and therefore in the outut ow over the entire adjustment ath), such that the agent is indi erent between the intial welfare level and that following the olicy change. 17

19 in GDP, aggregate consumtion, and the real exchange rate, all relative to their re-shock benchmark levels. a. An increase in ublic investment from traded outut: labor emloyment in the traded sector, as well as the share of traded outut in GDP increase instantaneously on imact of the shock, while aggregate consumtion declines. This haens because in the short run, with all rivate and ublic caital stocks xed instantaneously, the higher government sending on traded outut creates an increase in demand in that sector. As a result, the relative rice of traded goods increase instantaneously, causing a real dereciation of the exchange rate. This draws labor into the traded sector from the non-traded sector, increasing the ow of traded outut in the short run. On the other hand, even though the government sending will lead to a higher stock of ublic caital in the future, in the short run it reresents a resource withdrawal from the economy. of wealth causes the agent to instantaneously reduce consumtion. The resultant increase in the marginal utility Over time, as ublic investment leads to the gradual accumulation of the stock of ublic caital, the roductivity of labor and caital imrove in both sectors. Given the initial exansion of emloyment and outut in the traded sector, the higher roductivity along the transition ath ensures that it is sustained over time. The higher outut along the transition ath also ensures that consumtion increases in transition above its re-shock level after its initial decline. We also see from Figure 1 that the government sending increase generates a transitional behavior of the real exchange rate that is non-monotonic in nature, reresented by an U- shaed adjustment ath. Following its initial dereciation, the real exchange rate continues to dereciate in the short run but this trend is eventually reversed into a net long-run areciation. This haens because, following the shock, the full roductivity bene ts of the higher stock of ublic caital is not realized in the short run, given the slow convergence seeds of the state variables. However, the exectation of higher roductivity in the future requires that non-traded outut be transferred to the traded sector for rivate investment. Given intersectoral adjustment costs, this is a costly activity. Therefore, to reduce these adjustment costs, the non-traded sector accumulates caital faster than the traded sector. The marginal roduct of non-traded caital therefore increases at a slower rate than that of traded caital (comlemented by the transfer of labor to the traded sector as well), causing the real exchange rate to dereciate in the short run. Over time, as enough ublic caital is accumulated, and its roductivity bene ts are realized, the conventional Balassa-Samuelson e ect kicks in, and the real exchange rate areciates. 16 b. An increase in ublic investment from non-traded outut: The short-run resonse 16 Indeed, as we will see in section 4.3, when there are no intersectoral adjustment costs (h = 0), this non-monotonicity is absent from the ath of the real exchange rate. 18

20 of the economy to this shock is exactly the oosite of the corresonding resonse for the increase in sending from traded outut. The higher ublic sending in the non-traded sector increases the relative demand for non-traded goods, causing an instantaneous real areciation and reduction in labor emloyment in the traded sector. As resources get drawn into the non-traded sector, the share of traded outut in GDP also declines on imact of the sending shock. Given the instantaneous transfer of labor to the non-traded sector, the real exchange rate must over-shoot its long run equilibrium to equate the real return on labor in both sectors. In contrast to the case of sending on traded outut, aggregate consumtion now increases instantaneously, generating the observed short-run ositive correlation between government sending and consumtion that is observed in the data. Even though the sending shock generates a resource withdrawal e ect in the short run, the real areciation of the exchange rate increases the domestic consumtion of the traded good relative to the non-traded good, which has a net ositive e ect on aggregate consumtion. 17 In transition, for reasons noted above, the real exchange rate dereciates following its initial areciation. This draws resources back to the traded sector over time, increasing both labor emloyment in that sector as well as its share of outut in GDP. The time ath of the real exchange rate is again non-monotonic and has an U-shae, as the Balassa-Samuelson roductivity e ect from the higher stock of ublic caital eventually takes over. This causes a long-run real areciation of the exchange rate. c. An increase in the investment subsidy: The qualitative e ects of subsidizing the cost of transferring non-traded outut to the traded sector for investment are similar to that of an increase in ublic investment from the non-traded sector. The only di erence now is that since the cost of the transfer of resources to the traded sector is subsidized, the adjustment of the real exchange rate is less non-monotonic, with the short-run real areciation being sustained over time. The investment subsidy also generates a ositive short-run resonse of aggregate consumtion. When the non-traded sector is more caital intensive, the dynamic resonses to the three scal shocks are qualitatively similar, excet for the long-run adjustment of the real exchange rate. In this case, in shar contrast to the case when the traded sector is more caital intensive, the long-run real exchange rate dereciates for the two ublic investment shocks, underscoring the sensitivity of the real exchange rate dynamics to the sectoral intensity of rivate caital. 17 We will return to the issue of the short-run correlation between government sending and aggregate consumtion in section

21 3.3 Exchange Rate Dynamics: Sensitivity to Financing Policies In this section, we examine how sensitive the dynamic adjustment of the real exchange rate is to the three scal sending shocks, when di erent nancing olicies are used to balance the government s budget. Seci cally, we consider three tyes of nancing olicies: a. sending increase nanced by lumsum taxes (benchmark case) b. sending increase nanced by a tax on traded outut c. sending increase nanced by a tax on non-traded outut The short-run (instantaneous) and long-run resonses of the real exchange rate (relative to its re-shock equilibrium) are reorted in Table 3 and Figure 2. As we can see from these results, the underlying mode of nancing matters critically for both the short-run and longrun resonse of the real exchange rate. Since we have already discussed the resonse of the real exchange rate when sending increases are nanced by lumsum taxes, we will focus on the cases of distortionary tax- nancing in this section. When ublic investment is nanced by a tax on traded outut, irresective of which sector s outut the sending iminges on, the real exchange rate dereciates both in the short run as well as the long run. By contrast, the resonse is exactly the oosite when the same increase in ublic investment is nanced by a tax on non-traded outut: a real areciation in both the short run and long run. These results remain robust to the sectoral caital intensity. The intuition behind these contrasting resonses lie in the e ect of the sectoral income taxes on the relative demand for sectoral outut. A higher tax on traded (non-traded) outut, lowers the after-tax return from that sector s outut and discourages rivate investment. On the other hand, to the extent that the higher government sending it nances creates an augmented stock of ublic caital, it increases the long-run demand for rivate investment. If the second e ect dominates the rst, a tax on traded (non-traded) outut increases the long-run relative demand for traded (non-traded) outut for investment uroses. Therefore, the real exchange rate dereciates (areciates) as the relative rice of non-traded goods falls (rises). In the case of an increase in government sending on the investment subsidy, the real exchange rate areciates both in the short run as well as in the long-run, irresective of the mode of nancing. This indicates that the exansionary e ect of the subsidy dominates the distortionary e ects of the underlying tax olicies, thereby generating a net increase in demand for non-traded goods (since the subsidy is directed towards non-traded outut). 3.4 The Persistence of the Real Exchange Rate Figure 3 takes u the issue of the ersistence of the real exchange rate s dynamic adjustment (in terms of its deviations from the steady-state) and its imlications for emirical 20

22 analyses with relatively short time-series data. Most emirical studies of the real exchange rate use at most years of data to study its dynamics. On the other hand, the emirical literature has also documented the strong ersistence of real exchange rate deviations from PPP. This leads to the ossibility that in a relatively short time-series, what might look like a non-stationary rocess is actually stationary with a lot of ersistence. However, this may also lead to misleading redictions of the behavior of the real exchange rate in resonse to underlying shocks. Figure 3 lots the dynamic resonse of the real exchange rate for increases in ublic investment from traded outut ( gure 3A) and non-traded outut ( gure 3B) with each increase being nanced by lumsum taxes. The dynamic resonses are lotted for two scenarios: when the time eriod of analysis is (i) T = 40 eriods and (ii) T = 400 eriods. 18 As we can see, in the case where T = 40 eriods, the time-ath of the real exchange rate suggests that after its initial resonse (discussed above), the real exchange rate dereciates towards an "equilibrium," thus imlying that government sending shocks lead to a dereciation of the real exchange rate (as in Galstyan and Lane, 2009, or Ravn et al., 2011). However, once one considers the entire adjustment ath (T = 400 eriods), it is clear that the long-run resonse is actually a real areciation. The discreancy is due to the non-monotonicity of the relationshi between government sending and the real exchange rate. 3.5 The Short-run Correlation between Government Sending and Private Consumtion As discussed earlier, the correlation between government sending and consumtion in the short run has been the subject of much debate in the oen economy macro literature. The neoclassical deendent economy model tyically redicts a negative correlation between government sending and aggregate consumtion, due to the short-run resource withdrawal e ect and the consequent rise in the marginal utility of wealth. On the other hand, recent emirical studies have documented the resence of a ositive short-run correlation (see Ravn, et al., 2011). We consider this issue in Table 4 and Figure 4, and focus on the sensitivity of this redicted correlation with (i) the relative sectoral outut elasticity of ublic caital, and (ii) the sectoral comosition of government sending. The sending increases corresond to the benchmark olicy exercises we considered in section 3. The main di erence now is that we focus on three cases with resect to the sectoral outut elasticity of ublic caital: (i) ublic caital is more roductive in the traded 18 Since these results are generated using a numerical solution, we are agnostic about the interretation of the time "eriod," which could be at monthy, quarterly, or annual frequency. 21