A. Final Good Firms

The final consumption good, C_t, is a composite of intermediate goods produced by a continuum of monopolistically competitive firms both at home and abroad. We use j ∈ [0, 1] to index intermediate good firms as well as their products and prices. Final good firms operate under perfect competition and purchase domestically produced intermediate goods, Y_H,t(j), as well as imported intermediate goods, Y_F,t(j). Final good firms minimize expenditures subject to the following aggregation technology

where σ measures the trade price elasticity, i.e., the extent of substitution between domestically produced goods and imports for a given change in the terms of trade. The parameter ∊ > 1 measures the price elasticity across intermediate goods produced within the same country, while ω measures the weight of imports in the production of final consumption goods.

Expenditure minimization implies the following price indices for domestically produced intermediate goods and imported intermediate goods, respectively,

By the same token, the consumption price index is

Regarding the ROW, we assume an isomorphic aggregation technology. Further, the law of one price is assumed to hold at the level of intermediate goods.

B. Intermediate Good Firms

Intermediate goods are produced on the basis of the following production function

where α ∈ [0,1).⁴ H_t(j) measures the amount of labor employed by firm j.

Intermediate good firms operate under imperfect competition. We assume that price setting is constrained exogenously by a discrete time version of the mechanism suggested by Calvo (1983). Each firm has the opportunity to change its price with a given probability 1 – ξ. Given this possibility, a generic firm j will set P_H,_t(j) in order to solve

where Λ_t,t+k denotes the stochastic discount factor of the households who own firms, i.e., the ‘asset holders’; Y_t,_t+k(j) and H_t,t+k(j) denote demand and employment in period t + k, respectively, given that prices have been set optimally in period t. E_t denotes the expectations operator.

C. Households

We assume that there is a continuum of households [0, 1], a fraction 1 – λ of which are asset holders, indexed with a subscript ‘A’. These households own firms, and may trade one-period bonds both domestically and internationally. The remaining households (a fraction λ of the total) do not participate at all in asset markets, i.e., they are ‘non-asset holders’, and indexed with a subscript ‘N’. As in Bilbiie et al. (2008), differences between households are assumed to arise from their respective capacity to participate in asset markets, rather than from preferences.

Asset holders A representative asset-holding household chooses consumption, C_A,t, and supplies labor, H_A,t, to intermediate good firms in order to maximize

subject to the period budget constraint

where W_t denotes nominal wages, and T_t denotes nominal lump-sum taxes, in per capita terms. A_t and B_t are one-period bonds denominated in domestic and foreign currency, respectively. R_t and R_F,t denote the gross nominal interest rates on both bonds. Ψ_t is profits of intermediate good producers accruing to asset holders. ε_t denotes the nominal exchange rate measured in units of foreign currency per domestic currency. Ponzi schemes are ruled out by assumption.

We assume that the interest rate paid or earned on foreign bonds by domestic households is given by the exogenous world interest rate, $R_t^{*}$, and a ‘spread’ which decreases in the real value of bond holdings scaled by Y_t, the level of output defined below. Specifically, we set

This assumption ensures the stationarity of bond holdings (even for very small values of χ) and thus allows us to study the behavior of the economy in the neighborhood of a deterministic steady state.⁵

Non-asset holders A representative non-asset holding household chooses consumption, C_N,t, and supplies labor, H_N,t, to intermediate good firms in order to maximize its utility flow on a period-by-period basis

subject to the constraint that consumption expenditure equals net income

For non-asset holders, consumption equals disposable income in each period; hence they are also referred to as ‘hand-to-mouth consumers’.

D. Government

We specify the conduct of monetary policy by an interest rate feedback rule. Specifically, we assume that the central bank determines the nominal short-term rate following a Taylor-type rule:

where П _H,t = P_H,t/P_H,t−1 measures domestic inflation. Here and in the following, variables without time subscript refer to the steady-state value of a variable. A Taylor-type rule such as (11) provides a familiar and simple way to account for the role of monetary policy in the transmission of fiscal policy. Moreover, for ϕ → ∞, we can use (11) to approximate the flexible-price allocation as a reference point. Intuitively, if monetary policy reacts with infinite strength to any deviation of inflation from the target, it effectively precludes price dispersion, in line with flexible-price models.

Government spending is an aggregate of domestic intermediate goods:

We assume that intermediate goods are assembled so as to minimize costs. Thus the price index for government spending is given by P_H,t. Government spending is financed either through lump-sum taxes, T_t, or through issuance of nominal one-period debt, D_t. The period budget constraint of the government reads as follows

The time path of government spending and real taxes, T_R,t = T_t/P_t, is also determined by feedback rules, which we assume to take the following form

where ε_t measures an exogenous iid shock to government spending. The ψ-parameters capture the responsiveness of spending and taxes to government spending and debt. Note that for ψ_tg = 1, changes in government spending lead to a one-for-one increase in taxes, leaving government debt unchanged.

It is worth emphasizing that the analysis of government spending shocks has been typically conducted under the assumption that ψ_gd = 0, in which case government spending follows an exogenous process.⁶ Relaxing this restriction is essential for our own analysis, as we wish to trace the implications of debt-stabilizing spending dynamics for the transmission of fiscal shocks. Note in this context that (13) need not be interpreted strictly as an institutional rule constraining the fiscal authorities. Instead, like a Taylor rule for monetary policy, it may simply provide a description of fiscal policy-making, reflecting the complex set of incentives and constraints that govern the authorities’ decisions on the level of government spending.

E. Equilibrium

Equilibrium requires that firms and households behave optimally for given initial conditions, exogenously given developments in the ROW, and government policies. Moreover, market clearing conditions need to be satisfied. At the level of each intermediate good, supply must equal total demand stemming from final good firms, the ROW, and the government:

where $P_{H,t}^{*},P_t^{*}$, and $C_t^{*}$, denote the price index of domestic goods expressed in foreign currency, the foreign price level and foreign consumption, respectively.

As in Galí and Monacelli (2005), it is convenient to define an index for aggregate domestic output: $Y_t={\left({\displaystyle {\int }_0^1{Y}_t^{\frac{∊-1}{∊}}(j)\mathit{\text{dj}}}\right)}^{\frac{∊}{∊-1}}$. Substituting for Y_t(j) using (15) gives the aggregate relationship

In addition, the following has to hold

where $H_t={\displaystyle {\int }_0^1{H}_t(j)\mathit{\text{dj}}}$ is aggregate labor employed by domestic intermediate good firms.

Regarding asset markets, we assume that foreigners do not hold domestic bonds. Market clearing for domestic currency bonds therefore requires

The market for foreign currency bonds clears by Walras’ law.

We also define the trade balance in terms of steady-state output, and the real exchange rate as follows:

Note that an increase of Q_t corresponds to an appreciation of the real exchange rate.

A. Parameterization

Table 1 summarizes all parameter choices. A period in the model corresponds to one quarter. The discount factor β is set to 0.99. We assume that the coefficient of relative risk aversion, γ, and the inverse of the Frisch elasticity of labor supply, φ, take the value of one. The trade price elasticity σ is set equal to 2/3, which is in the range considered in the recent macroeconomic literature.⁷

Table 1.

Parameterization of the Model

Table 1.

Parameterization of the Model

Parameters		Value
Discount factor	β	0.99
Coefficient of risk aversion	γ	1
Inverse of Frisch elasticity	φ	1
Trade price elasticity	σ	2/3
Prob. of price fixed	ξ	0.75
Production function	α	0.63
Price elasticity of demand	∊	21
Import share of private demand	ω	0.15
Average spending share	gy	0.2
Autocorrelation spending	ψgg	0.9
Debt elast. of taxes	ψtd	0.02
Debt elast. of spending	ψgd	-0.02
Tax finance	ψtg	0.5
Monetary policy	ϕ	1.5
Debt elast. of interest rates	χ	0.00001
Non-asset holders	λ	0, 1/3

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Table 1.

Parameterization of the Model

Parameters		Value
Discount factor	β	0.99
Coefficient of risk aversion	γ	1
Inverse of Frisch elasticity	φ	1
Trade price elasticity	σ	2/3
Prob. of price fixed	ξ	0.75
Production function	α	0.63
Price elasticity of demand	∊	21
Import share of private demand	ω	0.15
Average spending share	gy	0.2
Autocorrelation spending	ψgg	0.9
Debt elast. of taxes	ψtd	0.02
Debt elast. of spending	ψgd	-0.02
Tax finance	ψtg	0.5
Monetary policy	ϕ	1.5
Debt elast. of interest rates	χ	0.00001
Non-asset holders	λ	0, 1/3

Price rigidities play a key role in the transmission of government spending shocks with spending reversals. We assume that ξ = 0.75, implying an average price duration of four quarters, within the range of values discussed, for example, by Nakamura and Steinsson (2008), if toward the higher end. Besides price stickiness, two additional features determine the extent to which the equilibrium allocation differs from the allocation that would obtain under flexible prices (flexible-price allocation, for short). First, the returns to labor, the only variable factor of production, are assumed to be decreasing, as indicated by α < 1. This assumption generates real rigidities. Second, the extent of these rigidities is further affected by the price elasticity of demand, measured by ∊. Specifically, we assume that α = 0.63 and ∊ = 21, implying a steady-state markup of 5 percent and a labor share of 60 percent.⁸

Regarding monetary policy, we assume that ϕ = 1.5, a value commonly employed by the literature. Regarding fiscal policy, we assume that changes in government spending are contemporaneously financed in equal part by taxes and debt, that is, we set ϕ_tg = 0.5. Further, we set ω = 0.15 and the average government spending share g_y = 0.20. This implies that imports account for 12 percent (because government spending is assumed to fall on domestic goods only) and government spending for 20 percent of steady-state output, in line with average values for the U.S. during the period 1980–2007. The parameter ψ_gg is set to 0.9, capturing the persistence of government spending deviations from trend documented by many VAR studies on U.S. data.

We set the two parameters that govern the responsiveness of taxes and government spending to debt equal to ψ_td = –ψ_gd = 0.02. The latter parameter is crucial for our account of the transmission mechanism. To the extent that contemporaneous taxes do not move one-for-one with government spending, some later response of taxes and/or spending is required to ensure public debt stability.⁹ In virtually all models of fiscal transmission, taxes are assumed—without further justification—to bear the entire burden of debt stabilization, i.e., ψ_gd = 0. This effectively makes the path of debt/taxes irrelevant for the real allocation of the economy (if λ = 0).

A fundamental passage in our analysis of fiscal policy is to recognize that at least some of the dynamic adjustment to a higher debt stock will fall on spending restraint. This proposition captures the reality of institutional and/or political constraints on governments’ capacity to raise taxes.¹⁰ It also finds support in empirical estimates of policy rules, which indicate a statistically significant adjustment of both spending and taxes in response to higher debt.¹¹ In our parameterization with ψ_gd = –0.02 and ψ_td = 0.02, an increase in government debt by 1 percentage point of GDP causes spending/taxes to be decreased/increased by 0.02 percentage points relative to their baseline trends.

In the last line of Table 1, we report the values for the parameter λ, i.e., the extent of participation in financial markets, which we vary across model simulations. Initially, we assume that all households have access to financial markets (λ = 0). Subsequently, we relax this assumption and posit λ = 1/3. Note that this is a relatively conservative number in light of the estimates reported by Galí et al. (2007), who reconsider estimates by Campbell and Mankiw (1989), and by Bilbiie et al. (2008).

B. Quantitative Analysis

In the following we analyze in detail the fiscal transmission mechanism under our specification of fiscal policy. The main finding is that, with anticipated spending reversals, the initial fiscal impulse exerts a stronger expansionary effect on output, by crowding in private consumption and depreciating the real exchange rate. This pattern of impulse responses conforms well with results from empirical studies that have long posed a challenge for macroeconomic theory. In traditional analyses based on the Mundell-Fleming model, government spending crowds-in private consumption, but also produces upward pressure on interest rates, which attracts capital inflows and thus appreciates the currency. The latter implication carries over to more recent models, whether neoclassical or new Keynesian (although the crowding-in of consumption does not!). In these models, given home bias in public demand, an increase in government spending is commonly shown to raise the international price of domestic output, i.e., appreciate the real exchange rate. The literature has recently paid increasing attention to this particular issue, as the response of real exchange rates provides a useful benchmark against which to assess models of fiscal transmission—see, for example, Ravn et al. (2007) and Monacelli and Perotti (2006).

In this spirit, this paper builds a case for refining our understanding of expenditure-side stimulus, going beyond the distinction of government spending by type (investment versus consumption, wages versus final goods—see Baxter and King (1993) and Finn (1998)) or according to the mix of tax versus deficit financing in the short run (see Ludvigson (1996)). Our main, novel argument is that much of the macroeconomic impact of fiscal stimulus depends on the own-dynamics of government spending, notably the extent to which temporary deficit spending is subsequently offset through spending cuts. In this regard, the common assumption that fiscal expansions lead to a one-for-one increase in the tax burden strikes us as an overly restrictive and implausible simplification. Indeed, by ignoring the possibility of spending reversals, macroeconomic models risk providing a distorted picture of fiscal policy transmission and the mechanics of expenditure-side stimulus.

Throughout, we consider an unanticipated increase in government spending by one percent of steady-state GDP. To focus on the core of the transmission mechanism, we report impulse responses for the following six variables: government spending, output, private consumption, short- and long-term real interest rates, and the real exchange rate. At the end of this section, we show an expanded set of impulse responses including other variables of interest.

Inspecting the mechanism

Figure 1 displays impulse responses for the parsimonious specification of our model where all households participate in asset markets (λ = 0). We gauge the importance of nominal rigidities by contrasting our baseline case featuring sticky prices (the corresponding impulse responses are denoted by solid lines) with a flexible-price allocation for the same economy (dashed lines).¹² In Figure 1, as well as in all the figures in the rest of this section, quantity variables are measured in percent of steady-state output; price variables (such as the real exchange rate, the interest rates, and real wages) are measured in percentage deviations from the steady-state level. Horizontal axes measure time in quarters.

Effect of Government Spending Shocks: Sticky Price vs. Flexible Price Allocation.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: Impulse responses to exogenous increase in government spending by one percent of GDP. Solid lines: ϕ = 1.5; dashed lines: ϕ = 500. Quantity variables are measured in percent of steady-state output. Price variables are measured in percentage deviations from the steady-state level. Horizontal axes measure time in quarters.

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Effect of Government Spending Shocks: Sticky Price vs. Flexible Price Allocation.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: Impulse responses to exogenous increase in government spending by one percent of GDP. Solid lines: ϕ = 1.5; dashed lines: ϕ = 500. Quantity variables are measured in percent of steady-state output. Price variables are measured in percentage deviations from the steady-state level. Horizontal axes measure time in quarters.

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Effect of Government Spending Shocks: Sticky Price vs. Flexible Price Allocation.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: Impulse responses to exogenous increase in government spending by one percent of GDP. Solid lines: ϕ = 1.5; dashed lines: ϕ = 500. Quantity variables are measured in percent of steady-state output. Price variables are measured in percentage deviations from the steady-state level. Horizontal axes measure time in quarters.

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The upper-left chart shows the dynamics of spending shocks, including a partial spending reversal. Spending rises on impact, but subsequently eases in response to higher outstanding debt and actually falls below trend levels some 12 quarters after the initial shock. To analyze the responses of all other variables, focus first on the flexible-price allocation.

The lower-left chart shows that the real short-term interest rate rises quite sharply on impact, dropping below steady-state levels no earlier than ten periods after government spending has fallen below trend. This path also drives the long-term real interest rate (shown in the lower-right chart), which compounds the infinite series of expected future short-term rates.¹³ Accordingly, the long-term rate increases considerably on impact, but then falls below steady-state levels around the time when spending drops below trend. Mirroring the path of this variable, private consumption initially drops; it recovers above trend levels not until the public spending increase has tapered off and the long rate fallen below steady-state level.¹⁴ Following the same pattern, the real exchange rate appreciates with above-trend public spending, and depreciates with below-trend public spending.¹⁵ Intuitively, the dynamic adjustment under flexible prices corresponds to a basic notion of efficiency, whereby prices induce a reallocation of private consumption over time, from periods when the government’s claim on domestic resources is above trend, to periods when it is below.

With nominal rigidities, real output bears a greater share of the initial adjustment to the shock. In Figure 1, this is manifest in short- and long-term real interest rates (solid lines) that are lower than under flexible prices, a greater rise in domestic production, an increase in private consumption, and a fall in the real exchange rate.

Anticipation effects are key to the transmission of fiscal policy displayed in Figure 1. Intuitively, our fiscal experiment could be interpreted as the combination of two different measures: one consists in the unexpected increase in government spending in the short run; the other in the announcement of a spending contraction to be implemented in the future. Price stickiness is not too consequential for the response of future demand and output to the preannounced spending cuts: with staggered price adjustment, many firms will have the opportunity to re-optimize their prices incorporating the expectation of public spending restraint. In contrast, price stickiness is crucial for the short-run effects of the temporary spending increase. As prices do not adjust sufficiently to reflect the scarcity of current output relative to greater aggregate demand, domestic output expands much more than under flexible prices. Indeed, with the central bank following a standard Taylor-type rule, the contractionary response of monetary policy is not strong enough to raise long-term interest rate up to the point of crowding out private consumption.

These dynamics, however, hinge not only on nominal rigidities, but also, and crucially so, on the debt-sensitivity of government spending. Figure 2 draws attention to this aspect by contrasting the baseline spending reversal (where the debt-sensitivity parameter of the spending rule is set to ψ_gd = –0.02) with the case of a debt-insensitive spending rule (ψ_gd = 0). Note that across the two experiments we maintain the sticky-price setup of the baseline specification.

Effect of Government Spending Shocks: Debt-Stabilizing vs. Debt-Insensitive Spending Rule.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: see Figure1. Solid lines: ψ_gd = –0.02; dashed lines: ψ_gd = 0.

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Effect of Government Spending Shocks: Debt-Stabilizing vs. Debt-Insensitive Spending Rule.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: see Figure1. Solid lines: ψ_gd = –0.02; dashed lines: ψ_gd = 0.

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Effect of Government Spending Shocks: Debt-Stabilizing vs. Debt-Insensitive Spending Rule.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: see Figure1. Solid lines: ψ_gd = –0.02; dashed lines: ψ_gd = 0.

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The dashed lines denote impulse responses for the debt-insensitive case. Observe that real shortterm interest rates in this case never fall below their steady-state level, in marked difference from the baseline specification denoted by solid lines. Hence long-term rates in the debt-insensitive case also remain consistently above their steady-state value after the spending shock; consumption falls; and the real exchange rate appreciates (see, for example, Linnemann and Schabert (2003)).

The specification without spending reversals implies that any spending increase leads to a one-for-one rise in the expected tax burden—a key assumption in most existing quantitative studies of fiscal transmission.¹⁶ By contrast, the debt-stabilizing spending rule puts some of the burden of adjustment on outlays, thereby reducing the need for significant tax increases. Under our parameterization, for instance, the government’s claim on domestic resources diminishes noticeably (by ca. 80 percent in net present value terms, at steady-state prices), as the higher debt stock caused by the initial rise in spending feeds back into spending cuts later on.

Yet the divergence between the two scenarios shown in Figure 2 cannot be attributed simply to differences in the size of the wealth shocks caused by the government’s claim on resources. To clarify this point, we reconsider the same scenarios under complete markets, implying that households are explicitly insured against the higher tax burden through a complete set of internationally traded state-contingent securities. In this case, domestic consumption (relative to foreign consumption) is tightly linked to the real exchange rate. Without the spending reversal, consumption falls in response to the government spending shock, while the real exchange rate appreciates—regardless of the fact that private wealth is now insulated from the shock. With the spending reversal, the exact opposite occurs. In other words, whether or not markets are complete, our baseline specification with debt-stabilizing spending dynamics predicts a positive consumption multiplier, associated with real depreciation. These results are shown in Figure A.1 in the appendix.

Another important point is worth stressing. In our model, spending reversals give rise to budget surpluses. However, it is the path of spending, not of deficits and surpluses, that makes a difference for fiscal transmission. This becomes clear from the fact that under a debt-insensitive spending rule, the timing of taxation is entirely irrelevant, given the assumed lump-sum nature of taxes. Instead, our analysis underscores the critical role of long-term interest rates in reflecting anticipated movements in public demand relative to domestic productive capacity.

The model with limited participation in asset markets

We now turn to our model specification where a fraction of households is without access to financial markets (λ = 1/3). This specification captures elements of the macroeconomy that are not key to the mechanism of spending reversals but important for fiscal policy in its own right. Specifically, the presence of ‘hand-to-mouth consumers’ reflects credit market imperfections that constrain households’ capacity to smooth consumption over time—imperfections which have come to the fore during the ongoing financial crisis and which provide a rationale for fiscal stabilization in the first place.

Figure 3 displays the impulse responses for this model economy. In addition to the variables displayed in Figures 1 and 2, Figure 3 also includes several additional variables of interest: consumption of asset holders and non-asset holders or ‘hand-to-mouth consumers’ (denoted by ‘A’ and ‘N’, respectively), the government budget balance, taxes, public debt, net foreign assets, the real wage, net exports, the short-term nominal interest rate, and domestic inflation (the latter two replacing the short-term real rate). As in the previous subsection, we compare a baseline case with spending reversals (solid lines) to the case of a debt-insensitive, exogenous path for spending, as commonly assumed in the literature (dashed lines).

Effect of Government Spending Shocks: Model with Limited Participation in Asset Markets (λ = 1/3).

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: see Figure 1.

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Effect of Government Spending Shocks: Model with Limited Participation in Asset Markets (λ = 1/3).

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: see Figure 1.

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Effect of Government Spending Shocks: Model with Limited Participation in Asset Markets (λ = 1/3).

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: see Figure 1.

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Without spending reversals, our numerical exercise shows that the presence of ‘hand-to-mouth consumers’ perse is not sufficient to generate a positive consumption multiplier. Indeed, as the long-term real interest rate remains above its steady-state value, the sharp contraction in the consumption of asset holders more than offsets the positive addition to demand from the non-asset holders. Note also that the real exchange rate appreciates, and the real wage response is positive.

With spending reversals, instead, hand-to-mouth consumers introduce important amplification effects. Private consumption rises much more on impact, implying a multiplier of about 0.4, close to the values reported by many empirical studies. Output also increases somewhat more than in the specifications shown in Figures 1 and 2. Interestingly, as the boost to aggregate demand from the fiscal stimulus is stronger, the long-term real interest rate initially rises, but this increase is short-lived, and followed by a prolonged decline below steady-state levels. The presence of hand-to-mouth consumers also alters the response of consumption, which no longer mirrors that of the long-term interest rate, and that of the real exchange rate. In particular, the strong impact increase in consumption coincides with a short-lived rise in long-term real interest rates and a brief real appreciation. Correspondingly, asset holders reduce their consumption initially, but the contraction of their demand is milder than in the case of debt-insensitive government spending.¹⁷

The stronger rise in private consumption reflects primarily the presence of hand-to-mouth agents, who consume more in response to the rise in current income—as real wages rise due to a shift in labor demand by firms constrained in price-setting.¹⁸ At the same time, the basic mechanism of the spending reversal remains essential for our results. Notably, it ensures that the response of the unconstrained agents in the economy will not ‘undo’ the effects of a fiscal expansion on aggregate demand via the hand-to-mouth agents. Indeed, both hand-to-mouth consumers and asset holders (after a few periods of initial retrenchment) now contribute to the rise in private consumption.

Figure 3 also displays the responses of additional variables of interest obtained under the extended model specification. Net exports deteriorate together with the government budget, corresponding to the notion of ‘twin deficits’.¹⁹ The stock variables net foreign assets and public debt evolve accordingly. Real wages increase strongly on impact, and fall below steady-state levels in sync with output.²⁰ The shock is mildly inflationary in the first 12 quarters or so, then the inflation response changes sign. This pattern is mirrored by the nominal interest rate, set according to the Taylor-type rule specified above.

A. VAR Specification

Our VAR model includes six variables: the first three are government spending, aggregate output, and private consumption, all in logs and per-capita terms; we also include a measure of the ex ante long-term real interest rate and the log of the real exchange rate; the sixth variable is the end-of-period stock of public debt scaled by quarterly GDP. Chung and Leeper (2007) and Favero and Giavazzi (2007) provide evidence suggesting that the omission of debt from the VAR model may lead to substantial bias in the estimated dynamics of fiscal policy shocks. Our theoretical analysis lends further support to this concern, as we emphasize the important feedback channel between debt and government spending.

We estimate our VAR model on quarterly time series data covering the period 1980:1–2007:4. While the choice of the sample period is chiefly determined by data availability (in particular, data on ex ante long-term real interest rates), it also has the advantage of focusing the analysis on a period in which the policy framework has arguably been fairly stable, especially as regards monetary policy. In the appendix we provide a detailed description of the data as well as results from alternative VAR specifications.

Drawing from the debate on the identification of fiscal shocks and the empirical characterization of fiscal policy transmission, we focus on two distinct strategies that have been widely employed in the literature.²¹ The first strategy, following Blanchard and Perotti (2002), relies on a structural VAR approach: identification is achieved by restricting the contemporaneous relationships between the fiscal and other variables included in the VAR. Specifically, government spending is assumed to be predetermined within the quarter. Under this assumption, the reduced-form residuals from a regression of government spending on the lags of all other variables in the VAR are identified as structural government spending shocks.

The second strategy, proposed by Ramey and Shapiro (1998), focuses on discrete fiscal policy changes related to wars and military build-ups. Indeed, these authors argue that such events come closest to economists’ notion of a truly exogenous source of variation in government spending. Ramey and Shapiro (1998) identify the dates at which the relevant military initiatives were first announced and trace the dynamic response of the economy to these announcements via dummy variables. Edelberg, Eichenbaum, and Fischer (1999) suggest an extended version of the Ramey-Shapiro approach using a VAR model.

For our own analysis, we follow recent contributions that have proposed a comprehensive framework encompassing both identification strategies—see Perotti (2007) and Ramey (2008). For a formal exposition of this framework, we draw on Monacelli and Perotti (2008). Specifically, letting g_t denote government spending and y_t a vector of additional variables of interest, we consider the following model

where κ_i0 and κ_i1, for i ∈ {1, 2}, denote coefficients on a constant and a linear time trend, respectively; d_t denotes a variable capturing exogenous fiscal events à la Ramey and Shapiro (‘military dates’); and under the assumption that g_t is predetermined relative to y_t, u_g,t can be given a structural interpretation as a government spending shock à la Blanchard and Perotti (‘VAR shock’).

As is well known, results based on the Blanchard-Perotti approach have generally been found to differ from those based on the Ramey-Shapiro approach. In particular, the former approach has typically led to findings of a positive consumption response to government spending, while studies based on the latter approach have tended to document a fall in consumption. Ramey (2008) provides further evidence showing that results differ systematically depending on whether military dates or VAR shocks are used to identify the effects of government spending. According to her interpretation, the divergence of results suggests that Blanchard and Perotti (2002)’s structural VAR does not accurately capture the timing of spending shocks. In this view, the measured VAR innovations are but the materialization of changes in government spending that have already been anticipated by the private sector.

Perotti (2007), instead, attributes the differences to a particular specification choice in Ramey’s analysis. Specifically, the model estimated by Ramey (2008) posits an equal number of lags for the military date variables in both of the above equations (q_2d = q_1d = 4). This, Perotti argues, amounts to interpreting as a result of the military shock all deviations of y_t from ‘normal’ during the entire first year following the shock. Yet such an assumption runs counter to the notion that Ramey’s military dates are informative about fiscal transmission as it works under ‘normal’ circumstances. On these grounds, Monacelli and Perotti (2008) only allow the contemporaneous value of the military date to enter the second equation (q_2d = 0, while q_1d = 6). Estimating a model on U.S. time series, they find that under this specification, the effects of VAR shocks and military dates are quite similar: most important, the response of private consumption is positive across both methodologies.

For our own baseline VAR model we adopt the same specification as Monacelli and Perotti (2008). As it turns out, however, the number of lags with which the military variable enters the non-fiscal equations of the model is largely inconsequential in our sample, anyway.

Finally, unlike the original dummy variable approach of Ramey and Shapiro (1998), we use the ‘new military variable’ introduced by Ramey (2008). It is defined as a continuous variable, where the military news (previously a binary variable) is quantified using the discounted value of the resulting change in government spending (scaled by the value of nominal spending from the previous quarter) as forecasted in real time by Business Week magazine. Relative to the original ‘military dates’, the new series also provides a richer account of exogenous military events that induced an adjustment in government spending.²²

B. Results

We begin by presenting evidence on the fiscal transmission mechanism under the ‘VAR shock’ approach of Blanchard and Perotti. In Figure 4, we show the effects of a VAR shock normalized such that government spending increases by one percent of GDP. The horizontal axis indicates quarters after the shock. All quantity variables are expressed in output units, so that responses may be interpreted as multipliers. The real exchange rate is measured in percent deviations from its pre-shock level, while the response of the long-term real interest rate is measured as deviations from the pre-shock level in quarterly percentage points. Throughout, the solid line indicates the point estimate, and the shaded area represents a 90-percent confidence interval obtained by bootstrap sampling.

Fiscal Policy Transmission According to VAR Model: Effects of VAR Shock.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: solid line indicates point estimate; grey area: 90 percent confidence interval obtained by bootstrap sampling. The horizontal axis indicates quarters, the vertical axes measure deviations from trend in percentage points of trend output (in case of quantities); percent deviations from the pre-shock level (real exchange rate); and deviations from the pre-shock level in terms of quarterly percentage points (real interest rate).

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Fiscal Policy Transmission According to VAR Model: Effects of VAR Shock.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: solid line indicates point estimate; grey area: 90 percent confidence interval obtained by bootstrap sampling. The horizontal axis indicates quarters, the vertical axes measure deviations from trend in percentage points of trend output (in case of quantities); percent deviations from the pre-shock level (real exchange rate); and deviations from the pre-shock level in terms of quarterly percentage points (real interest rate).

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Fiscal Policy Transmission According to VAR Model: Effects of VAR Shock.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: solid line indicates point estimate; grey area: 90 percent confidence interval obtained by bootstrap sampling. The horizontal axis indicates quarters, the vertical axes measure deviations from trend in percentage points of trend output (in case of quantities); percent deviations from the pre-shock level (real exchange rate); and deviations from the pre-shock level in terms of quarterly percentage points (real interest rate).

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Focus first on our main variable of interest, government spending itself. While we find a fairly persistent response, spending clearly undershoots its trend value about four years after the shock. Interestingly, both the initial increase in government spending and its subsequent reversal are statistically significant. This is a notable finding in light of our theoretical analysis of spending reversals. It also matches a similar earlier result documented by Chung and Leeper (2007). Importantly, these authors compare results from relatively small VAR systems to those from a more comprehensive VAR which includes government debt. They find that government spending appears to be partially ‘self-correcting’ according to the more comprehensive VAR only, underscoring the importance of controlling for debt as a state variable.²³ Our finding of a significant spending reversal also squares well with the results of Galí and Perotti (2003), documenting a responsiveness of government spending to public debt for OECD countries.

Output responds in a statistically significant way with an impact multiplier of about one. It later falls below trend, mirroring the path of government spending. Private consumption increases significantly for the first few quarters after the shock. The response is mildly hump-shaped and peaks at about 0.5 percent of GDP. From a quantitative point of view, these results for output and consumption are close to earlier findings by Blanchard and Perotti (2002) and Galí et al. (2007), among many others.

Another notable result is the response of the long-term real interest rate. After rising sharply (though insignificantly) on impact, the interest rate falls below its pre-shock level after about six quarters. This finding again mirrors results that have been reported elsewhere in the literature, but have long been regarded as difficult to reconcile with the presumed theoretical case for a persistent interest rate increase.²⁴ By contrast, the estimated response of the real interest rate is quite consistent with the prediction of our theoretical model with government spending reversals, as shown in Figure 3.

Next, the lower-left chart shows the response of the real exchange rate, which depreciates sharply and significantly, remaining below trend for a long period after the initial spending shock. Very similar evidence has been documented earlier by Kim and Roubini (2008), Monacelli and Perotti (2006), and Ravn et al. (2007). Enders et al. (2008) also document a fall in the real exchange rate, while using a different identification scheme based on sign restrictions. Indeed, empirical studies have documented real depreciation after a positive government spending shock not only for the U.S., but also for Australia, and the UK.²⁵

Finally, the lower-right chart shows the response of public debt, which increases significantly and persistently, peaking around five years after the occurrence of the shock. This result suggests that the increase in government spending is to a considerable extent debt-financed, in line with evidence in Galí et al. (2007), who document a significant increase in the public deficit, as well as in Bilbiie et al. (2008), who also document a significant increase in public debt. Interestingly, this significant build-up of debt also reinforces the rationale for the kind of spending reversals at the core of this paper.²⁶

Overall, we find the impulse responses to a VAR shock in line with the predictions of our model. Not only do our VAR results reproduce well-known earlier findings, notably the crowding-in of private consumption and the depreciation of the real exchange rate in response to a positive government spending shock. They also lend support to the two main implications of our account of the fiscal transmission mechanism with spending reversals: i) government spending falls below trend after an initial and somewhat persistent increase, the switch occurring after about four years; ii) long-term interest rates, while rising upon impact, also fall below their pre-shock level in the second year after the shock, i.e., before the actual spending reversal. In the appendix, we also provide results from an extensive sensitivity analysis showing that our findings are robust across various alternative specifications of the VAR model: excluding debt or long-term interest rates; excluding the linear time trend; extending the sample; changing the number of lags for the military variables; and considering an alternative ‘nominal’ VAR model which includes the federal funds rate and inflation rather than long-term real interest rates and public debt.

As discussed above, our VAR model encompasses the ‘military variable’ approach pioneered by Ramey and Shapiro. In the VAR shock approach which we have focused on thus far, these military variables serve as additional controls. However, we now turn to Ramey’s full-fledged alternative, in which military events are the only identified source of fiscal shocks. Figure 5 displays the estimated responses to such a military event.

Fiscal Policy Transmission According to VAR Model: Effects of Military Event.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: see Figure 4.

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Fiscal Policy Transmission According to VAR Model: Effects of Military Event.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: see Figure 4.

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Fiscal Policy Transmission According to VAR Model: Effects of Military Event.

Citation: IMF Working Papers 2009, 106; 10.5089/9781451872538.001.A001

Notes: see Figure 4.

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Remarkably, we find that government spending actually falls in response to the military event, rising back above its trend level only after about 20 quarters. This finding may seem paradoxical, as the military events are meant to capture episodes of defense-related fiscal expansions. What estimates for our sample suggest instead is that any increase in military expenditure that may be associated with the military event tends to be more than offset by simultaneous expenditure cuts elsewhere. Although surprising, such intratemporal spending dynamics are certainly conceivable, perhaps even reflecting the same kind of overall financing constraints that we see at the root of intertemporal spending reversals. In any case, given this initial result, it is important to interpret all other estimated impulse responses as responses to a negative, rather than positive, spending shock. Indeed, the time path of government spending in Figure 5 is essentially a mirror image (with flipped sign) of the ‘VAR shock’ path studied earlier, including the occurence of a spending reversal after some four to five years.

With this in mind, observe that the responses of the other variables in Figure 5 are quite consistent with those obtained for the VAR shock, i.e., the co-movement of these other variables with government spending is quite similar across identification schemes. In particular, consumption falls initially, and the real exchange appreciates. Likewise, the responses of public debt and the long-term interest rate mirror those obtained under the VAR shock approach. Together, this set of responses further confirms key predictions from our theoretical model: the dynamics of fiscal transmission with spending reversals appears to match the time-series evidence, whether it is based on the identification scheme of Blanchard and Perotti (2002) or that of Ramey and Shapiro (1998).

Some additional comments on the robustness of the results using the military-event approach are in order. To begin with, the finding that government spending falls in response to a military event is not specific to our analysis: Ramey (2008) herself also reports a significant decline of government spending. However, in her analysis, government spending starts to rise more quickly again, and peaks between 4 and 8 quarters after the military date. We find that the difference relative to our own findings is explained by three factors. The first is the sample period, as Ramey considers time series starting in the 1940s. The second factor is the number of lags of the military event variable. While our results are quite robust to allowing for more lags of this variable in the non-spending equations of the VAR model, the inclusion of more lags has a mild impact on the time at which government spending is seen to start rising above trend; with more lags of the military variables, this happens after about 16 quarters, instead of 20 quarters (see Figure A.4 in the appendix). The third factor is the inclusion of public debt and the real exchange rate in the model, consistent with our theoretical account of the transmission mechanism. In particular, the real exchange rate may proxy for fluctuations in long-term real rates which effectively drive consumption decisions.²⁷ Moreover, public debt is arguably a key determinant for future adjustments of government spending. In sum, to the extent that the results we obtain under the military dates approach are sensitive to some specification choices, there are good reasons for the particular choices we consider.