Emerging markets such as China, India, and Brazil have recently embarked on an ambitious expansion of government spending, mainly on public infrastructure such as roads, airports, rail, power supply, 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 public spending to reign in government debt, although spending on infrastructure has remained a potential area of expansion. In an era of global economic integration, the dynamic effects of these policies on external prices and competitiveness will be of critical importance for both developing and developed countries. Understanding this relationship in the context of a dynamic general equilibrium model is the central objective of this paper.
The link between government spending and the real exchange rate has been the subject of a growing but inconclusive literature in international macroeconomics. Specifically, the predictions of the theoretical literature on this issue are sharply at odds with corresponding empirical findings, mainly in three areas:1
(1) The first issue concerns the effect of a change in government spending on the real exchange rate, especially in the short run. The theoretical literature, based predominantly on the neoclassical dependent economy model, typically treats government spending as representing public consumption, thereby impinging on the economy as a pure demand shock. Consequently, the real exchange rate is predicted to appreciate in the short run in response to an increase in government spending. The long-run real exchange rate, on the other hand, remains unaffected, being determined solely by supply-side factors such as sectoral productivity. In the short run, an increase in government consumption increases the demand for non-traded goods and their relative price (the real exchange rate appreciates). This effect is offset over time by a gradual depreciation of the exchange rate to its initial level. By contrast, several recent empirical studies have documented that government spending actually generates a real depreciation of the exchange rate in the short run.2 However, empirical studies seldom distinguish between government investment and consumption, thereby providing little understanding of why the stylized facts are at odds with theoretical predictions. Given that public consumption and investment might impinge on resource allocation in dramatically different ways, it is not clear whether the composition of government spending might be driving the discrepancy between theory and facts. A recent contribution by Galstyan and Lane (2009) attempts to address this discrepancy, but by limiting their focus only to the long-run steady-state, and thereby abstracting away from intertemporal issues, they are not able to resolve the controversy over the short-run and transitional effects of government spending on the real exchange rate.
(2) Second, a large empirical literature has documented the strong persistence of real exchange rate fluctuations, implying very long periods 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 predicted deviations of the exchange rate (from equilibrium) generated by theoretical models are very short-lived and monotonic, with implausibly fast speeds of convergence. This discrepancy may be potentially resolved by focusing on government spending on infrastructure, rather than consumption. There are three key factors in this context that may explain both persistence and non-linearity in the adjustment of the real exchange rate: first, since public infrastructure is accumulated gradually over time, the short run resource withdrawal effects described above in (1) must be evaluated against the long-run effects on private productivity, thereby indicating an intertemporal relationship between government spending and the real exchange rate. Second, it may be costly for investors to re-allocate private capital across sectors in response to the long-run productivity benefits of public investment. Third, the effects of underlying taxation policies that finance such spending must also be considered as a source of both non-linearity and persistence. These aspects of public policy are largely ignored in the existing literature. Given the persistence of real exchange rate movements observed in the data, these effects may not be fully captured by limited time-series data or a steady-state analysis.
(3) Finally, a contentious policy issue in the literature relates to the short-run correlation between government spending and private consumption. Theoretical models predict a short-run negative correlation: by withdrawing resources from the private sector, government spending raises the marginal utility of wealth which, in turn, leads agents to increase labor supply and reduce the consumption of all normal goods in the short run. By contrast, the empirical literature has documented a positive correlation between public spending and private consumption in the short run.4 Again, focusing on government investment rather than consumption may help resolve the issue at hand. An increase in government spending which is allocated to the creation of infrastructure capital will raise the long-run productivity of both private capital and labor. Private agents, anticipating this long-run increase in their returns from private investment and labor supply (thereby anticipating higher income in the long-run) can choose to increase their rate of private consumption in the short run, by borrowing from their future (higher) expected income.
In this paper, we examine the mechanism through which government spending, specifically on public infrastructure, and accompanying financing policies affect the dynamics of the real exchange rate. In doing so, we also attempt to reconcile the neoclassical dependent economy model with observed empirical regularities. We employ a two-sector open economy model with government-provided infrastructure capital (henceforth “public capital”) augmenting the productivity of private capital and labor in both the traded and non-traded sectors.5 This aspect of our model relates to Galstyan and Lane (2009), but with three key differences. First, while they restrict their analysis to the steady-state, we conduct a full dynamic analysis that characterizes the intertemporal trade-offs in the adjustment of the real exchange rate to government spending shocks. Second, while Galstyan and Lane (2009) assume that all public investment impinges only on non-traded output and is financed by lumpsum taxes, we focus on a full range of fiscal issues, such as the sectoral composition of government investment and the effects of distortionary taxes on sectoral income. We also parameterize our model to compare the effects of government consumption with investment. Third, we introduce intersectoral adjustment costs to generate the observed persistence in the adjustment of the real exchange rate. Specifically, we assume that it is costly for agents to transfer private capital from the non-traded to the traded sector for investment purposes. While Galstyan and Lane (2009) assume a costless transfer of capital across sectors, we follow Morshed and Turnovsky (2004) in introducing convex costs of transferring private capital 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 effects of government spending 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 public capital and intersectoral adjustment costs enables us to identify plausible conditions under which the two-sector dependent open economy model yields qualitative predictions that are consistent with stylized facts.7
The analytical structure we employ yields a fifth-order non-linear dynamic system with three state and two jump variables and hence requires a numerical solution. We consider three types of government spending policies: (i) an increase in public investment from traded output, (ii) and increase in public investment from non-traded output, and (iii) an investment subsidy that reduces the cost of transferring capital from the non-traded to the traded sector. We assume that these spending increases can be financed by (i) a lumpsum tax (or government debt), (ii) a distortionary tax on traded output, or (iii) a distortionary tax on non-traded output. Our numerical experiments reveals some interesting results that are qualitatively consistent with stylized facts:
(a) In the presence of a gradually accumulating stock of public capital and intersectoral adjustment costs, government spending generates a persistent and non-monotonic U-shaped adjustment path of the real exchange rate (following its instantaneous response), thereby generating sharp intertemporal trade-offs.8 The intuition for this result stems from the fact that an increase in government spending on infrastructure and its long-run productivity benefits increase the demand for private investment in the short run in both sectors. Since the transfer of private capital across sectors is a costly activity, the non-traded sector accumulates private capital faster than the traded sector to reduce intersectoral adjustment costs (which are determined by the outflow of resources from the non-traded sector per unit of installed capital in that sector). Consequently, the marginal product of private capital in the non-traded sector increases at a slower rate than the corresponding marginal product in the traded sector (due to diminishing returns), causing a real depreciation of the exchange rate in the short and medium term.
(b) The instantaneous, transitional (the length and depth of the U-shaped adjustment), and steady-state (long-run) response of the real exchange rate to an increase in public investment depends critically on (i) the sectoral composition of government spending on infrastructure (i.e., whether the spending increase impinges on traded or non-traded output), (ii) the underlying financing policy (lumpsum tax or sectoral income tax), (iii) the sectoral intensity of private capital, and (iv) the sectoral output elasticity of public capital. We also identify conditions under which a short-run depreciation of the real exchange rate is reversed into a net real appreciation in the long-run (through the Balassa-Samuelson effect). Given the persistence of the U-shaped adjustment path, we argue that empirical studies that document a long-run real depreciation of the exchange rate in response to an increase in government spending may be picking up only a transitional effect.
(c) The observed short-run positive correlation between government spending and consumption is generated when (i) public capital is more productive in the traded sector and (ii) the increase in public investment is from non-traded output. Further, an investment tax-credit (subsidy) also generates this positive correlation. These results are derived in the absence of a home bias in consumption and indicate that the observed positive correlation between government spending and consumption is not inconsistent with the neoclassical model.
In summary, we characterize the structural conditions under which the qualitative predictions of the neoclassical open economy model can be reconciled with stylized facts regarding the relationship between government spending, private consumption, and the dynamics of the real exchange rate. We also check the sensitivity of the adjustment path of the real exchange rate to (a) the sectoral output elasticity of public capital, (b) the elasticity of substitution in production, and (c) intersectoral adjustment costs. In a recent contribution, Ravn et al.(2011) develop an open economy model with deep habit persistence and imperfect competition to explain the short-run correlations between government spending, the real exchange rate, and private consumption. We view our contribution as complementary to theirs, but without sacrificing the dependent economy framework on which the large bulk of theory on this issue has been developed.
The rest of the paper is organized as follows. Section 2 develops a canonical two-sector dependent economy model with public capital and intersectoral adjustment costs, Section 3 presents the numerical calibration of the model and the policy experiments, Section 4 discusses the sensitivity analysis, and Section 5 concludes.
2 The Analytical Framework
We consider a small open economy with an infinitely-lived representative agent who maximizes utility from the consumption of a traded good and a domestically produced non-traded good. The agent accumulates wealth over time through an internationally traded bond and faces a perfect world capital market with an exogenous interest rate. There are two production sectors in this economy, namely the traded goods sector and the non-traded goods sector. Each sector uses three factors of production: private capital, labor, and a government-provided stock of public capital (infrastructure). The stock of public capital represents a non-excludable and non-rival public good that enhances the productivity of private capital and labor in both production sectors through a spillover effect. The government appropriates fractions of both traded and non-traded output for public investment, and finances this spending using distortionary income taxes (levied on incomes in both sectors) as well as lumpsum taxes (or debt). Finally, we will also assume that all private investment takes place in the non-traded sector, but it is costly for the agent to transfer resources to the traded sector for the creation of private capital 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 price of the non-traded good is the real exchange rate, with an increase denoting a real appreciation and vice-versa.
2.1 Resource Allocation in the Private Sector
The representative agent’s intertemporal utility function is given by
subject to a flow budget constraint
where, CT and CN denote the consumption of the traded and non-traded good, respectively. B denotes an internationally traded bond which earns an exogenous world interest rate, r. The agent produces output YT in the traded-goods sector and YN in the non-traded sector. IN represents private investment in the non-traded sector and Ω(.) is the intersectoral adjustment cost incurred by the agent to transfer resources for investment in the traded sector. The agent pays taxes on output produced in both sectors, with traded output being taxed at the rate τT and non-traded output being taxed at the rate τN. The agent also pays a lumpsum tax, TL, and receives an investment subsidy s, targeted towards reducing the cost of converting non-traded output to investment in the traded sector. Finally, the relative price of the non-traded good, i.e., the real exchange rate, is denoted by p.
The rate of accumulation of private capital in each sector is given by
where KT is the stock of private capital in the traded sector, KN is the corresponding stock in the non-traded sector, and X is the proportion of non-traded output that is allocated to private investment in the traded sector. The cost of transferring non-traded output to the traded sector for investment is given by
where h is the adjustment cost parameter.9
The agent is endowed with one unit of time for work, which it uses to allocate labor supply to the two sectors. The labor market equilibrium condition is then given by
where LT is the employment in the traded sector and LN is the corresponding measure in the non-traded sector.
Production of final goods in the traded and non-traded sectors uses a standard neoclassical technology and three factors: sectoral private capital and labor, and the aggregate stock of public capital, KG, provided by the government:
The stock of public capital generates services that are complementary to the private factors in each sector, enhancing their productivity along the transition path and in the long run. The market-clearing condition in the non-traded sector is given by
where GN represents the proportion of non-traded output used by the government for public investment. Private capital in the non-traded sector then evolves according to
The agent chooses the rate of consumption 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 policy variables and the stock of public capital as given, and at the beginning of the planning horizon, is endowed with an initial stock of bonds and private capital, given by B(0), KT(0), and KN(0). The current-value Hamiltonian function is
where λ is the shadow price of wealth held in the traded bond, and
The first-order conditions (8a) and (8b) equate the marginal utility of consumption 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 open economy facing a perfect world capital market: the rate of time preference must equal the world interest rate. This restricts the shadow price of wealth to be a constant over time, and therefore
From (8a) and (8b), we can derive the policy functions for sectoral consumption:
An increase in the marginal utility of wealth reduces the consumption of both traded and non-traded good, as the agent increases labor supply to offset for the increase in
A real appreciation draws resources into the non-traded sector reducing traded-sector, employment. An increase in the stock of private capital in the traded sector raises the marginal product of labor in that sector, raising employment. Exactly the opposite happens when non-traded capital increases. Finally, the effect of a higher stock of public capital on employment in the traded sector is ambiguous and depends on the relative productivity of public capital in the traded sector, η—φ. If public capital is more productive in the traded sector, employment in that sector increases, and vice versa.11
To obtain the rate of private investment in the traded-goods sector, we differentiate (8g) with respect to time, while taking note of (8e) and (8f):
2.2 The Public Sector
The government spends both traded and non-traded output to generate new public investment in public capital. Let sectoral spending by the government be given by Gi (i = T, N). The spending rules for each sector are
where gi represents the rate of public investment from sector i (i = T, N). As such, gi represent policy variables for the government which can be used to alter the rate of sectoral private investment. These can also be thought of as representing the composition of government spending on infrastructure. Public capital accumulates according to
where δG represents the rate of depreciation of public capital.12 The government maintains a balanced budget at all points of time, using tax revenues to finance spending on infrastructure and the investment subsidy:
The evolution of the current account is obtained by combining (2) with (11):
2.3 Macroeconomic Equilibrium
The core equilibrium dynamics are represented by a fifth-order non-linear differential equation system with three state variables, KT, KN, and KG and two jump variables, p and X:
The steady-state is attained when
At the steady-state equilibrium, the current account is given by
where the “~” denotes a steady-state quantity for an endogenous variable. To solve the model, we will assume that at the initial pre-shock steady-state, the economy does not hold any debt or credit, i.e.,
The linearized dynamics around this initial steady-state can be expressed as
where Ẕ′ = (KT, KN, KG, p, X) is the vector of state and controls, Λ is a 5x5 matrix of linearized coefficients, and
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 optimal (linearized) time paths of the endogenous variables in the vector ẕ′ takes the following canonical form:
where A1, A2, and A3 represent the constants associated with the stable eigenvalues μ1, μ2, and μ3, respectively, and Vji (i = 1, 2, 3) denote the normalized eigenvectors associated with each stable eigenvalue, where we apply the normalization v1i = 1. Linearizing the current account equation in (12) around the steady-state equilibrium, we can derive the following (linearized) differential equation for the current account:
with all the partial derivatives evaluated at the steady-state. Using (17) in (18), solving the resulting differential equation, and imposing the transversality condition for the traded bond from (8i) leads to the following adjustment path for the current account
Under the assumption that B(0) = 0, (19a) can be solved for the steady-state level of the current account,
3 Numerical Analysis
The analytical model described in section 2 is too complex for a closed-form solution, and therefore must be evaluated numerically. To solve the model, we propose the following functional forms for the utility and production functions:
where γ is related to the intertemporal substitution in consumption, e = 1/(1—γ) and θ is the relative importance of non-traded consumption in the agent’s utility function. The overall productivities of the traded and non-traded sectors are determined by an exogenous component given by AT and AN, respectively, and the aggregate stock of public capital in the economy, provided by the government. The parameters η and ϕ denote the sectoral output elasticities of public capital. Given the homogeneity of the production functions, a and ϕ represent the capital intensity in the traded and non-traded sectors, respectively, Finally, ρ is related to the elasticity of substitution between private capital and labor in the production function by s = 1/(1 + ρ). The case where s = 1 (ρ = 0) approximates the familiar Cobb-Douglas production function.
3.1 The Benchmark Equilibrium
Table 1A describes the parameterization of the benchmark economy. The preference parameter γ is chosen to yield an intertemporal elasticity of substitution in consumption of 0.4, consistent with the evidence reviewed by Guevenen (2006). The choice of θ = 0.5 ensures that there is no home bias in consumption and each good has the same weight in the utility function. The world interest rate is set at 6 percent. The exogenous productivity parameters AT and AN are chosen to yield a plausible benchmark equilibrium. The output elasticity of public capital is set to 0.15 in each sector as a benchmark specification. There is a large empirical 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 specification. We will, of course, conduct a sensitivity analysis by differentially varying the sectoral elasticities. The intersectoral adjustment cost parameter is set at h = 30, following the calculations of Morshed and Turnovsky (2004). Again, this parameter will be subject to a sensitivity analysis. We assume a rate of public investment from traded output, gT = 0.02 and from non-traded output, gN = 0.07 to ensure that about 4.6% of aggregate output is spent on infrastructure investment, which is also the long-run average for most OECD countries. Given this specification, about 21 percent of government spending comes from the traded goods sector, while 79 percent comes from the non-traded sector. We also assume that there are no distortionary taxes or subsidies in the benchmark equilibrium and all government spending is financed through lumpsum taxes. The benchmark equilibrium is calibrated for the Cobb-Douglas production function.
|γ = -1.5, β = r = 0.06, θ = 0.5|
|AT = 1.5, AN = 1, η = ϕ = 0.15, h = 30, δG = 0.05|
|gT = 0.02, gN = 0.07, τT = τN = 0, s = 0|
|B. PRE-SHOCK STEADY-STATE QUANTITIES|
|Traded Sector More Capital Intensive (a = 0.35, ϕ = 0.25)||14.258||8.827||3.051||7.965||0.451||0.487||0.477||0.213||3.624||0.252||0.046||1.912|
|Non-Traded Sector More Capital Intensive (a = 0.25, ϕ = 0.35)||12.286||19.847||3.659||6.642||0.523||0.487||0.477||0.213||4.775||0.191||0.046||1.139|
Table 1B reports the benchmark steady-state equilibrium for two cases: (i) the traded sector is more capital intensive than the non-traded sector (α = 0.35, φ = 0.25) and (ii) the non-traded sector is more capital intensive than the traded sector (α = 0.25, φ = 0.35).14 For example, in the case where the traded sector is more capital intensive, the capital-labor ratio in the traded and non-traded sectors are about 14.26 and 8.83, respectively. The capital-output 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 output in GDP is about 0.49. The share of consumption of each good in GDP is about 0.48 (since there is no home bias). The steady-state aggregate capital-output ratio is 3.62 and the ratio of public to private capital is 0.25. The long-run real exchange rate is about 1.91.
3.2 Fiscal Policy Shocks
Table 2 reports the long-run effects of three fiscal policy shocks on the macroeconomy and the resultant change in intertemporal welfare. We subject the benchmark equilibrium in Table 1B to the following three government spending shocks:
a. An increase in public investment from traded output: gT increases permanently from 0.02 to 0.05.
b. An increase in public investment from non-traded output: gN increases permanently 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 permanently from 0 to 0.1.
NOTE: All results are reported relative to their pre-shock equilibrium levels
|A. TRADED SECTOR MORE CAPITAL-INTENSIVE|
|KT / LT||pkN / LN||LT||YT / Y||C||Y||p||ΔW (%)|
|a. ΔgT||1.072||1.079||1.087||1.081||1.002||1.085||1.010||+ 0.122|
|b. ΔgN||1.071||1.078||1.044||1.041||1.005||1.081||1.010||+ 0.217|
|c. Δs||1.117||1.044||1.036||1.034||1.013||1.046||1.038||- 0.063|
|B. NON-TRADED SECTOR MORE CAPITAL-INTENSIVE|
|KT / LT||pkN / LN||LT||YT / Y||C||Y||p||ΔW (%)|
|a. ΔgT||1.079||1.071||1.063||1.068||0.998||1.066||0.992||+ 0.126|
|b. ΔgN||1.080||1.072||1.033||1.035||1.001||1.069||0.992||+ 0.197|
|c. Δs||1.116||1.031||1.018||1.019||1.010||1.029||1.026||- 0.011|
In policy changes a and b, we calibrate the increase in government spending to ensure that in each case total government investment rises from its benchmark rate of 4.6 percent to about 6 percent of GDP. In all three cases, the spending increase is financed by an appropriate adjustment of lumpsum taxes to balance the government’s budget. For the benchmark case, using a non-distortionary financing instrument has the advantage of decoupling the effects of spending from revenues. The long-run impact of these fiscal shocks are reported for two alternative scenarios: where the traded sector is more capital intensive and vice versa. The steady-state changes in variables are reported relative to their pre-shock benchmark levels, so that a value greater than one indicates an increase and vice versa. The effect on welfare is reported as a percentage change.15
As is evident from Table 2A and 2B, all three government spending shocks, being tied to investment activity, have an expansionary effect on the economy in the long-run, with the capital-labor ratio increasing in both sectors, along with aggregate consumption and GDP. The share of labor employment in the traded sector and traded output in GDP increase in all three cases, indicating that the non-traded sector shrinks relative to the traded sector. Intertemporal welfare improves when government spending is directed towards public investment. However, the investment subsidy generates a net welfare loss for the economy. We also note that the investment subsidy is the least expansionary of the three fiscal spending shocks. The long-run change in the real exchange rate deserves some comment. For the cases where government spending increases public investment, the long-run real exchange rate appreciates when the traded sector is more capital intensive. By contrast, when the non-traded sector is more capital intensive, there is a long-run real depreciation. In the case of the investment subsidy, the real exchange rate appreciates irrespective of the sectoral capital intensity.
The intuition behind the above results can be better understood by a depiction of the dynamic response of the economy to these shocks. This is illustrated in Figure 1, which plots the time paths of labor employment in the traded sector, the share of traded output in GDP, aggregate consumption, and the real exchange rate, all relative to their pre-shock benchmark levels.
FIGURE 1.Government Spending Shocks (Lumpsum Tax-financed)
a. An increase in public investment from traded output: labor employment in the traded sector, as well as the share of traded output in GDP increase instantaneously on impact of the shock, while aggregate consumption declines. This happens because in the short run, with all private and public capital stocks fixed instantaneously, the higher government spending on traded output creates an increase in demand in that sector. As a result, the relative price of traded goods increase instantaneously, causing a real depreciation of the exchange rate. This draws labor into the traded sector from the non-traded sector, increasing the flow of traded output in the short run. On the other hand, even though the government spending will lead to a higher stock of public capital in the future, in the short run it represents a resource withdrawal from the economy. The resultant increase in the marginal utility of wealth causes the agent to instantaneously reduce consumption. Over time, as public investment leads to the gradual accumulation of the stock of public capital, the productivity of labor and capital improve in both sectors. Given the initial expansion of employment and output in the traded sector, the higher productivity along the transition path ensures that it is sustained over time. The higher output along the transition path also ensures that consumption increases in transition above its pre-shock level after its initial decline.
We also see from Figure 1 that the government spending increase generates a transitional behavior of the real exchange rate that is non-monotonic in nature, represented by an U-shaped adjustment path. Following its initial depreciation, the real exchange rate continues to depreciate in the short run but this trend is eventually reversed into a net long-run appreciation. This happens because, following the shock, the full productivity benefits of the higher stock of public capital is not realized in the short run, given the slow convergence speeds of the state variables. However, the expectation of higher productivity in the future requires that non-traded output be transferred to the traded sector for private investment. Given intersectoral adjustment costs, this is a costly activity. Therefore, to reduce these adjustment costs, the non-traded sector accumulates capital faster than the traded sector. The marginal product of non-traded capital therefore increases at a slower rate than that of traded capital (complemented by the transfer of labor to the traded sector as well), causing the real exchange rate to depreciate in the short run. Over time, as enough public capital is accumulated, and its productivity benefits are realized, the conventional Balassa-Samuelson effect kicks in, and the real exchange rate appreciates.16
b. An increase in public investment from non-traded output: The short-run response of the economy to this shock is exactly the opposite of the corresponding response for the increase in spending from traded output. The higher public spending in the non-traded sector increases the relative demand for non-traded goods, causing an instantaneous real appreciation and reduction in labor employment in the traded sector. As resources get drawn into the non-traded sector, the share of traded output in GDP also declines on impact of the spending 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 spending on traded output, aggregate consumption now increases instantaneously, generating the observed short-run positive correlation between government spending and consumption that is observed in the data. Even though the spending shock generates a resource withdrawal effect in the short run, the real appreciation of the exchange rate increases the domestic consumption of the traded good relative to the non-traded good, which has a net positive effect on aggregate consumption.17 In transition, for reasons noted above, the real exchange rate depreciates following its initial appreciation. This draws resources back to the traded sector over time, increasing both labor employment in that sector as well as its share of output in GDP. The time path of the real exchange rate is again non-monotonic and has an U-shape, as the Balassa-Samuelson productivity effect from the higher stock of public capital eventually takes over. This causes a long-run real appreciation of the exchange rate.
c. An increase in the investment subsidy: The qualitative effects of subsidizing the cost of transferring non-traded output to the traded sector for investment are similar to that of an increase in public investment from the non-traded sector. The only difference 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 appreciation being sustained over time. The investment subsidy also generates a positive short-run response of aggregate consumption.
When the non-traded sector is more capital intensive, the dynamic responses to the three fiscal shocks are qualitatively similar, except for the long-run adjustment of the real exchange rate. In this case, in sharp contrast to the case when the traded sector is more capital intensive, the long-run real exchange rate depreciates for the two public investment shocks, underscoring the sensitivity of the real exchange rate dynamics to the sectoral intensity of private capital.
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 fiscal spending shocks, when different financing policies are used to balance the government’s budget. Specifically, we consider three types of financing policies:
a. spending increase financed by lumpsum taxes (benchmark case)
b. spending increase financed by a tax on traded output
c. spending increase financed by a tax on non-traded output
The short-run (instantaneous) and long-run responses of the real exchange rate (relative to its pre-shock equilibrium) are reported in Table 3 and Figure 2. As we can see from these results, the underlying mode of financing matters critically for both the short-run and long-run response of the real exchange rate. Since we have already discussed the response of the real exchange rate when spending increases are financed by lumpsum taxes, we will focus on the cases of distortionary tax-financing in this section. When public investment is financed by a tax on traded output, irrespective of which sector’s output the spending impinges on, the real exchange rate depreciates both in the short run as well as the long run. By contrast, the response is exactly the opposite when the same increase in public investment is financed by a tax on non-traded output: a real appreciation in both the short run and long run. These results remain robust to the sectoral capital intensity. The intuition behind these contrasting responses lie in the effect of the sectoral income taxes on the relative demand for sectoral output. A higher tax on traded (non-traded) output, lowers the after-tax return from that sector’s output and discourages private investment. On the other hand, to the extent that the higher government spending it finances creates an augmented stock of public capital, it increases the long-run demand for private investment. If the second effect dominates the first, a tax on traded (non-traded) output increases the long-run relative demand for traded (non-traded) output for investment purposes. Therefore, the real exchange rate depreciates (appreciates) as the relative price of non-traded goods falls (rises).
NOTE: All results are reported relative to their pre-shock equilibrium levels
|A. TRADED SECTOR MORE CAPITAL INTENSIVE|
|I. a. ΔgT (Lumpsum tax-financing)||0.998||1.007|
|b. ΔgT (tax on traded output)||0.978||0.976|
|c. ΔgT (tax on non-traded output)||1.007||1.041|
|II. a. ΔgN (Lumpsum tax-financing)||1.022||1.007|
|b. ΔgN (tax on traded output)||1.001||0.976|
|c. ΔgN (tax on non-traded output)||1.030||1.039|
|III. a. Δs (Lumpsum tax-financing)||1.012||1.038|
|b. Δs (tax on traded output)||1.008||1.033|
|c. Δs (tax on non-traded output)||1.013||1.043|
|B. NON-TRADED SECTOR MORE CAPITAL INTENSIVE|
|I. a. ΔgT (Lumpsum tax-financing)||0.999||0.992|
|b. ΔgT (tax on traded output)||0.979||0.963|
|c. ΔgT (tax on non-traded output)||1.004||1.037|
|II. a. ΔgN (Lumpsum tax-financing)||1.022||0.992|
|b. ΔgN (tax on traded output)||1.0004||0.963|
|c. ΔgN (tax on non-traded output)||1.029||1.034|
|III. a. Δs (Lumpsum tax-financing)||1.013||1.026|
|b. Δs (tax on traded output)||1.011||1.022|
|c. Δs (tax on non-traded output)||1.014||1.031|FIGURE 2.Government Spending and the Real Exchange Rate: Sensitivity to Financing Policies
In the case of an increase in government spending on the investment subsidy, the real exchange rate appreciates both in the short run as well as in the long-run, irrespective of the mode of financing. This indicates that the expansionary effect of the subsidy dominates the distortionary effects of the underlying tax policies, thereby generating a net increase in demand for non-traded goods (since the subsidy is directed towards non-traded output).
3.4 The Persistence of the Real Exchange Rate
Figure 3 takes up the issue of the persistence of the real exchange rate’s dynamic adjustment (in terms of its deviations from the steady-state) and its implications for empirical analyses with relatively short time-series data. Most empirical studies of the real exchange rate use at most 25-30 years of data to study its dynamics. On the other hand, the empirical literature has also documented the strong persistence of real exchange rate deviations from PPP. This leads to the possibility that in a relatively short time-series, what might look like a non-stationary process is actually stationary with a lot of persistence. However, this may also lead to misleading predictions of the behavior of the real exchange rate in response to underlying shocks.
FIGURE 3.Government Spending, the Persistence of the Real Exchange Rate, and the Time Horizon
(α = 0.35, ϕ = 0.25)
Figure 3 plots the dynamic response of the real exchange rate for increases in public investment from traded output (figure 3A) and non-traded output (figure 3B) with each increase being financed by lumpsum taxes. The dynamic responses are plotted for two scenarios: when the time period of analysis is (i) T = 40 periods and (ii) T = 400 periods.18 As we can see, in the case where T = 40 periods, the time-path of the real exchange rate suggests that after its initial response (discussed above), the real exchange rate depreciates towards an “equilibrium,” thus implying that government spending shocks lead to a depreciation of the real exchange rate (as in Galstyan and Lane, 2009, or Ravn et al., 2011). However, once one considers the entire adjustment path (T = 400 periods), it is clear that the long-run response is actually a real appreciation. The discrepancy is due to the non-monotonicity of the relationship between government spending and the real exchange rate.
3.5 The Short-run Correlation between Government Spending and Private Consumption
As discussed earlier, the correlation between government spending and consumption in the short run has been the subject of much debate in the open economy macro literature. The neoclassical dependent economy model typically predicts a negative correlation between government spending and aggregate consumption, due to the short-run resource withdrawal effect and the consequent rise in the marginal utility of wealth. On the other hand, recent empirical studies have documented the presence of a positive 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 predicted correlation with (i) the relative sectoral output elasticity of public capital, and (ii) the sectoral composition of government spending.
Instantaneous response of total consumption relative to its pre-shock equilibrium level:
|A. TRADED SECTOR MORE CAPITAL INTENSIVE|
|η = ϕ = 0||η = 0.15, ϕ = 0.05||η = 0.05, ϕ = 0.15|
|ΔgT (Lumpsum tax-financing)||0.980||0.998||0.987|
|ΔgN (Lumpsum tax-financing)||0.985||1.008||0.996|
|Δs (Lumpsum tax-financing)||1.004||1.005||1.004|
|B. NON-TRADED SECTOR MORE CAPITAL INTENSIVE|
|η = ϕ = 0||η = 0.15, ϕ = 0.05||η = 0.05, ϕ = 0.15|
|ΔgT (Lumpsum tax-financing)||0.981||0.997||0.986|
|ΔgN (Lumpsum tax-financing)||0.987||1.008||0.995|
|Δs (Lumpsum tax-financing)||1.005||1.006||1.006|FIGURE 4.Government Spending and Consumption: Sensitivity to the Sectoral Elasticity of Public Capital
The spending increases correspond to the benchmark policy exercises we considered in section 3. The main difference now is that we focus on three cases with respect to the sectoral output elasticity of public capital: (i) public capital is more productive in the traded sector (η = 0.15, ϕ = 0.05), (ii) public capital is more productive in the non-traded sector (η = 0.05, ϕ = 0.15), and (iii) public capital has no productivity benefits in either sector (η = ϕ = 0), so that an increase in government spending represents entirely government consumption. Table 4 reports the instantaneous response of aggregate consumption relative to its pre-shock benchmark, and Figure 4 plots the entire dynamic adjustment of consumption relative to its pre-shock level.
As we can see, these experiments throw up both negative and positive correlations between the short-run response of consumption and the underlying spending shock. Specifically, the results indicate that the following conditions for a positive correlation between government spending and short-run consumption that is observed in the data:
(a) public investment in infrastructure must impinge on non-traded output, and
(b) public capital must be at least as productive in the traded sector as it is in the non-traded sector (η ≥ ϕ).
The intuition is drawn from our discussion in Section 3.2 above. An increase in public spending from non-traded output generates a short-run resource withdrawal effect in that sector, which in turn causes an instantaneous real appreciation of the exchange rate. As non-traded goods become more expensive on the margin, the agent substitutes away from non-traded consumption towards consumption of the traded good. In addition, if public capital is at least or more productive in the traded sector, then the long-run productivity benefits of public investment for the traded sector and its eventual expansion (through the Balassa-Samuelson effect) causes a large instantaneous increase in consumption of traded output, which more than offsets the short-run decline in non-traded consumption. As a result, aggregate consumption increases in the short run.
We also find that when government spending takes the form of an investment subsidy targeted towards lowering intersectoral adjustment costs, aggregate consumption increases in the short run. In this particular case, we observe a positive correlation irrespective of the sectoral output elasticity of public capital. The above results are also robust to the sectoral capital intensity in production (Table 4B, Figure 4B).
4 Sensitivity Analysis
This section conducts a sensitivity analysis of the dynamic response of the real exchange rate to government spending shocks to variations in three deep structural parameters of the model: (i) the sectoral output elasticities of public capital, η and ϕ, (ii) the elasticity of substitution between private capital and labor in production, s = 1/(1 + ρ), and (iii) the intersectoral adjustment cost parameter, h.
4.1 Sectoral Output Elasticity of Public Capital
As in the previous section, we consider three cases: (i) η = 0.15, ϕ = 0.05, (ii) η = 0.05, ϕ = 0.15, and (iii) η = ϕ = 0. Figure 5 depicts the adjustment path of the real exchange rate relative to its pre-shock equilibrium. The relative sectoral output elasticity of public capital is a critical determinant of the dynamics of the real exchange rate. When public investment impinges on traded output, the short-run exchange rate appreciates (depreciates) both in the short run as well as the long run when public capital is more (less) productive in the traded sector. When public capital is not productive, the increase in spending from traded output represents government consumption. Since this is a pure demand shock, the real exchange rate depreciates in the short run, but returns to its pre-shock equilibrium in the long-run. In this case, government spending has no impact on the long-run real exchange rate, which is a well-known result in the literature.
FIGURE 5.Government Spending and the Real Exchange Rate: Sensitivity to the Sectoral Elasticity of Public Capital
When public investment draws on non-traded output, the short run exchange rate appreciates, irrespective of the relative sectoral elasticity of public capital, with the appreciation being the largest when public capital is more productive in the traded sector. In the long-run however, the sectoral elasticity matters. When public capital is more productive for the traded sector, the short run appreciation is sustained in the long-run. By contrast, when the non-traded sector benefits more from public capital, the short run appreciation is reversed over time into a long-run depreciation. When government spending is not productive for either sector and represents public consumption, the real exchange rate converges back to its pre-shock equilibrium following the initial appreciation.
When government spending takes form of an investment subsidy, the time path of the real exchange rate is more robust, with a short-run and long-run appreciation of the real exchange rate, with the short-run rate under-shooting the long-run equilibrium. All the above results are robust to variations in the sectoral capital intensity in production.
4.2 Elasticity of Substitution in Production
Figure 6 plots the response of the real exchange rate to the three underlying government spending shocks for three values of the elasticity of substitution in production between private capital and labor: (i) s = 0.75, (ii) s = 1, and (iii) s = 1.25.
FIGURE 6.Government Spending and the Real Exchange Rate: Sensitivity to the Elasticity of Substitution in Production
We see from figure 6 that the larger is the elasticity of substitution in production, larger is the short-run and long-run response of the real exchange rate to a government spending shock, but the qualitative responses remain robust to the benchmark cases discussed in section 3. Further, the higher the elasticity of substitution in production, the more persistent is the adjustment of the real exchange rate.
4.3 Intersectoral Adjustment Costs
Figure 7 illustrates the sensitivity of the real exchange rate dynamics generated by the three fiscal spending shocks to the magnitude of intersectoral adjustment costs. We consider three cases: (i) h = 0 (costless transfer of capital across sectors), (ii) h = 30 (benchmark specification), and (iii) h = 60. As is evident from the plots, the intersectoral adjustment costs do not affect the steady-state response of the real exchange rate. This is because, in the steady-state, there is no new investment in private capital in the traded sector, i.e.,
FIGURE 7.Government Spending and the Real Exchange Rate: Sensitivity to Intersectoral Adjustment Costs
In this paper, we have analyzed the mechanism through which government spending policies, specifically on public infrastructure, affect the dynamics of the real exchange rate. While much of the literature has previously focused on the effects of government consumption in the context of the neoclassical dependent open economy model, government investment and financing policies have received far less attention. Moreover, many of the predictions of the neoclassical model with respect to the effect of government spending on private consumption and the real exchange rate are at variance with stylized facts. We propose a framework in this paper based on the neoclassical model that reconciles many of its qualitative predictions with the data.
Specifically, we introduce government spending in a two-sector open economy in the form of (i) a gradually accumulating stock of productivity-augmenting infrastructure capital, and (ii) an investment subsidy that reduces the cost of transferring capital from the non-traded to the traded goods sector. We further assume that the government can finance this spending on investment by a range of distortionary and non-distortionary tax instruments. Our results indicate that in the presence of intersectoral adjustment costs, government spending shocks generate a non-monotonic U-shaped adjustment path for the real exchange rate. Given the persistence of this adjustment path, a transitional depreciation that lasts for several years after the incidence of the shock can be more than reversed over time, as the resource withdrawal effects of government spending in the short run are dominated by its productivity impact over time. Whether government spending leads to a short-run (long-run) depreciation or appreciation depends critically on (i) the sectoral composition of the spending, (ii) the underlying financing policy, (iii) the sectoral capital-intensity in production, and (iv) the sectoral output elasticities of public capital. Characterizing these structural conditions provides a foundation from which the divergence between theory and empirics can be reconciled. Robustness checks are conducted for the elasticity of substitution in production and the intersectoral adjustment costs.
Our model is also able to predict the observed positive short-run correlation between government spending and private consumption when (i) public capital is at least as productive in the traded sector as it is in the non-traded sector, and (ii) government investment impinges on non-traded output. An investment subsidy also generates this positive correlation in the short run. This is an important result, since the neoclassical open economy model, in the absence of a home bias, has difficulty in predicting this positive correlation. Though Ravn et al. (2011) propose an alternative framework with deep habit persistence and monopolistic competition, we show that the neoclassical model, with some plausible modifications, can still be reconciled with the data.
AgenorP. and J.Aizenman (2010) “Aid, volatility, and poverty traps.” Journal of Development Economics 911–7.
AgenorP. (2011) Public capital growth and welfare: Analytical foundations for public policy. Princeton University Pressforthcoming.
AschauerD.A. (1989) “Is public expenditure productive?” Journal of Monetary Economics 23177–200.
AseaP. and E.Mendoza (1994) “The Balassa--Samuelson model: a general-equilibrium appraisal.” Review of International Economics 2244–267.
BarroR.J. (1990) “Government spending in a simple model of endogenous growth.” Journal of Political Economy 98S103–S125.
BlanchardO. and R.Perotti (2002) “An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output.” Quarterly Journal of Economics 1171329–1368.
BomP. and J.Lithgart (2010) “What have we learned from three decades of research on the productivity of public capital?” MimeoTilburg University.
BrockP. (1996) “International transfers, the relative price of non-traded goods and the current account.” Canadian Journal of Economics 29163–180.
BrockP. and S.Turnovsky (1994) “The dependent economy model with both traded and nontraded capital goods.” Review of International Economics 2306–325
CaporaleG.D.Ciferri and A.Girardi (2011) “Fiscal shocks and real exchange rate dynamics: Some evidence for Latin America.” Journal of International Money and Finance 30709–723.
ChatterjeeS.G.Sakoulis and S.Turnovsky (2003) “Unilateral capital transfers, public investment, and economic growth.” European Economic Review 471077–1103.
ChatterjeeS. and S.Turnovsky (2007) “Foreign aid and economic growth: the role of flexible labor supply.” Journal of Development Economics 84507–533.
CerraV.S.Tekin and S.Turnovsky (2010) “Foreign transfers and real exchange rate adjustments in a financially constrained dependent economy.”Open Economies Review 20147–181.
CheungY. and K.Lai (2000) “On cross-country differences in the persistence of real exchange rates.” Journal of International Economics 50375–397.
ChowdhuryI. (2004) “Sources of exchange rate fluctuations: empirical evidence from six emerging market countries.” Applied Financial Economics 14697–705.
EdwardsS. and M.Savastano (1999) “Exchange rates in emerging economies: What do we know? What do we need to know.” NBER Working Paper 7228.
EngelC. (1993) “Real Exchange Rates and Relative Prices: An Empirical Investigation.” Journal of Monetary Economics 3235–50.
EngelC. (1999) “Accounting for U.S. real exchange rate changes.” Journal of Political Economy 107507–538.
FatasA. and I.Mihov (2001) “The effects of fiscal policy on consumption and employment: theory and evidence.” ManuscriptINSEAD.
FisherW.H. and S.J.Turnovsky (1998) “Public investment, congestion, and private capital accumulation.” Economic Journal 108399–413.
FrootK. and K.Rogoff (1995) “The EMS, the EMU, and the Transition to a Common Currency.” NBER Macroeconomics Annual 6269–317.
GalstyanV. and P.Lane (2009) “The composition of government spending and the real exchange rate.” Journal of Money Credit and Banking 411233–1249.
GlommG. and B.Ravikumar (1994) “Public investment in infrastructure in a simple growth model.” Journal of Economic Dynamics and Control 181173–87.
GramlichE.M. (1994) “Infrastructure investment: a review essay.” Journal of Economic Literature 321176–96.
GuvenenF. (2006) “Reconciling conflicting evidence on the elasticity of intertemporal substitution: A macroeconomic perspective.” Journal of Monetary Economics 531451–1472.
KimS. and N.Roubini (2008) “Twin Deficit or Twin Divergence? Fiscal Policy, Current Account, and Real Exchange Rate in the U.S.” Journal of International Economics 74362–383.
KnetterM. (1993) “International comparisons of pricing to market behavior.”American Economic Review 83473–486.
MonacelliT. and R.Perotti (2006) “Fiscal Policy, the Trade Balance, and the Real Exchange Rate: Implications for International Risk Sharing.”ManuscriptIGIER, Universit’a Bocconi.
MorshedM. and S.Turnovsky (2004) “Sectoral adjustment costs and real exchange rate dynamics in a two-sector dependent economy.” Journal of International Economics 63147–177.
ObstfeldM. (1989) “Fiscal deficits and relative prices in a growing world economy.” Journal of Monetary Economics 23461–484.
ObstfeldM. (1993) “Model Trending Real Exchange Rates.” CIDER Working Papers 11.
RavnM.S.Schmitt-Grohe and M.Uribe (2011) “Explaining the effects of government spending shocks on consumption and the real exchange rate.” NBER Working Paper 13328.
RiojaF. (2003) “Filling potholes: Macroeconomic effects of maintenance vs. new investments in public infrastructure.” Journal of Public Economics 872281–2304.
SenP. and S.Turnovsky (1990) “Investment tax credit in an open economy.” Journal of Public Economics 42277–309.
TaylorM. (1995) “The economics of exchange rates.” Journal of Economic Literature 3313–47.
TaylorM.D.Peel and L.Sarno (2001) “Non-linear mean reversion in real exchange rates: Toward a solution to the purchasing power parity puzzles.” International Economic Review 421015–1042.
TurnovskyS. (1997) International macroeconomic dynamics. The MIT PressCambridge.
Van WincoopE. (1993) “Structural adjustment and the construction sector.”European Economic Review 37177–201.
The theoretical literature has relied predominantly on the two-sector dependent open economy model; prominent contributions include Obstfeld (1989), van Wincoop (1993), Brock and Turnovsky (1994), Brock (1996), and Morshed and Turnovsky (2004). The empirical link between fiscal policy and real exchange rate fluctuations have been examined, among others, by Obstfeld (1993), Asea and Mendoza (1994), Chowdhury (2004), Kim and Roubini (2008), Galstyan and Lane (2009), Caporale et al. (2011) and Ravn et al. (2011).
See Engel (1993, 1999), Knetter (1993), Froot and Rogoff (1995), Taylor (1995), Edwards and Savastano (1999), and Cheung and Lai (2000) for some early contributions. For non-linearities in the adjustment path of the real exchange rate, see Taylor et al. (2001).
There is a voluminous literature on the role of public capital in affecting economic growth, starting with the work of Aschauer (1989) and Barro (1990). Important theoretical contributions include Glomm and Ravikumar (1994), Fisher and Turnovsky (1998), Rioja (2003), and Agenor and Aizenman (2007); see Agenor (2011) for a comprehensive review. Gramlich (1994) and Bom and Lithgart (2010) provide reviews of the corresponding empirical literature.
Morshed and Turnovsky (2004) provide several examples from post-World War II Western Europe to motivate the presence of intersectoral adjustment costs, such as the costly retro-fitting of war-time industries to produce consumer goods in the post-war era. Further, many developing countries adopt industrial policies that directly or indireclty subsidize private investment in their export sectors. These include the creation of Special Economic Zones (SEZ), subsidies for R&D, tax breaks, etc. We model the subsidy as an investment tax credit for transfering capital from the non-traded sector to the traded sector. The investment tax-credit has also been studied for the one-sector dependent economy model; see, for example, Sen and Turnovsky (1990).
A recent contribution by Cerra et al.(2010) also examines the effects of financing public investment by foreign aid. However, they model the flow of public investment as being relevant for production rather than the accumulated stock of public capital, along with a costless transfer of capital across sectors. The distinction between the stock and flow specifications turns out to be crucial for the predictions of the model. Chatterjee et al.(2003) and Chatterjee and Turnovsky (2007) also analyze the issue of infrastructure financing by foreign aid, but in the context of one-sector, one-good models of the open economy, which abstract away from issues related to the exchange rate.
Non-linearities in the adjustment path 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 path, albeit from a very different source (intersectoral adjustment costs and a gradually accumulating stock of public capital).
Note that h = 0 represents the standard Heckscher-Ohlin specification, where it is costless to transfer capital across sectors. On the other hand, when h → ∞, the model converges to the specific factors model, with capital being immobile across sectors.
The details of these results are available on request from the authors.
The details of these results are available on request from the authors.
Since this is a neoclassical model with a stationary steady-state, and the government is not an optimizing entity, we need a positive rate of depreciation for public capital to close the model. Otherwise, spending on public investment would have to arbitrarily jump to zero at the steady-state, which could not be justified with a passive government.
It is well known in the dependent open economy models that the dynamics depend critically on the sectoral capital intensities; for a detailed discussion see Turnovsky (1997).
Changes in welfare levels are computed by an equivalent variation in output across steady states, i.e., we determine the required change (in percentage terms) in the initial output level (and therefore in the output flow over the entire adjustment path), such that the agent is indifferent between the intial welfare level and that following the policy change.
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 path of the real exchange rate.
We will return to the issue of the short-run correlation between government spending and aggregate consumption in section 3.5.
Since these results are generated using a numerical solution, we are agnostic about the interpretation of the time “period,” which could be at monthy, quarterly, or annual frequency.