Fiscal Adjustment and Inflation Targetingin Less Developed Countries

Edward F. Buffi e and Manoj Atolia

January 2015

Abstract

Inflation targeting may not be viable in LDCs where policy makers rely too heavily on cuts

in infrastructure investment to balance the budget. Using a mix of analytical and numerical

methods, we demonstrate that the equilibrium ceases to be saddlepoint stable under active

policy when infrastructure cuts account for 30-70% of fiscal adjustment and the return on

infrastructure exceeds a comparatively low threshold value. The result is robust to the form

of the Taylor rule, the degree of real wage flexibility, the initial level of debt, the choice of a

balanced-budget or debt-targeting rule, and the q-elasticity of private investment spending.

Keywords: Taylor principle, inflation targeting, infrastructure investment, non-Ricardian

fiscal policy.

JEL codes: E31, E52, E53, E63.

• Edward F. Buffi eDepartment of EconomicsWylie Hall 105Indiana UniversityBloomington, IN 47405United States

Email: ebuffi e@indiana.edu

• Manoj Atolia288 Bellamy BuildingDepartment of EconomicsFlorida State UniversityTallahassee, FL 32306

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1. Introduction and Overview

. . . at times of fiscal retrenchment . . . investment is "the least rigid componentof expenditure" (De Haan et al., 1996). In support of this last assertion, Echeverryet al. (2004) report recent data from the Colombian ministry of finance estimating at97% the proportion of the central government budget that is "inflexible," meaning thatthe authorities cannot exercise discretion over most budgetary items in the short run.According to this account, the only flexible component is public investment. (Suescun,2005)

Thus, given the practical diffi culties to (i) raise tax and non-tax revenues rapidly, and(ii) alter current expenditures . . . governments have little choice but to adjust publicinvestment to maintain fiscal balance in the face of shocks. (Dessus and Varoudakis,2013)

But this anti-investment bias of fiscal austerity is not exclusive to Latin America. Thesame phenomenon has been documented in a variety of country by numerous observers. . . (Perry et al., 2008b)

However, as explained in Section II, it has proved diffi cult . . . to prevent publicinvestment from bearing the brunt of required fiscal adjustment. A number of factorshave contributed to such an outcome. First, political economy considerationssuggest that cutting current spending is often diffi cult . . . (IMF, 2004)

Most models of inflation targeting assume that lump-sum transfers adjust to satisfy the

government budget constraint. While this assumption may be tenable in certain cases, it

strongly contradicts the empirical evidence that infrastructure investment bears the brunt

of fiscal adjustment in emerging market economies and low-income countries. Estimates

by Gavin and Perotti (1997) and data presented in Calderon et al. (2003), Serven (2007),

and Easterly et al. (2008) show that cuts in infrastructure investment consistently account

for 50 - 80% of deficit reduction in Latin America.1 The World Bank (1988, 1994a), Hicks

(1991), Jonakin and Stephens (1999), and Estache (2004) report equally large numbers

for LDCs in other regions, and numerous case studies/empirical estimates affi rm that in-

frastructure spending is far and away the most volatile component of public expenditure

at business cycle frequencies (Gavin and Perotti, 1997; IMF, 2004; Easterly et al., 2008,

Dessus and Varoudakis, 2012). Consistent with this, Ilzetzki and Vegh (2008) and Dessus1 Offi cial data put infrastructure’s share of fiscal adjustment at 40 - 70%. This figure is biased downward, however,by the misclassification of operations and and maintenance spending as part of recurrent expenditure instead ofinvestment.

1

and Varoudakis (2013) find that reductions in infrastructure investment account for 79 -

86% of expenditure cuts in panel datasets comprised of 27 and 124 LDCs.2 The literature

abounds with political economy explanations of why tax rates and current expenditure are

highly rigid in the short run3 and with documented episodes in which 100% of fiscal ad-

justment falls on infrastructure investment.4 Development macroeconomics boasts of only

a few stylized facts. Regrettably, slashing expenditure on roads, power, and water systems

to protect other items in the budget is one of the most robust.

In this paper we argue that inflation targeting (IT) may not work when policy makers

rely too heavily on investment cuts to balance the budget. The general nature of the threat

is easy to discern. When the central bank raises the real interest rate to combat an inflation

shock, the fiscal deficit worsens (ex ante) both because interest payments on the debt increase

and because tax revenues fall. The induced decrease in infrastructure investment reinforces

the contractionary effect of higher interest rates on aggregate demand. But lower investment

today translates into less infrastructure and higher costs of production tomorrow. Under

Calvo pricing, the impact on current inflation depends on the change in the present value

of real marginal costs. The key parameter in the present value calculation is the real return

on infrastructure, which determines how much future marginal costs increase. If the return

is zero, the Taylor principle is safe as cuts in infrastructure investment are indistinguishable

from cuts in government consumption. But if the return is high, the sharp increase in future

marginal cost causes inflation to rise even though aggregate demand and real output fall.

It is a short step from this to the conclusion that the macroeconomy is either unstable or

highly vulnerable to sunspot equilibria. IT requires more than subordination of fiscal policy

to monetary policy; it also requires supporting fiscal adjustment of the right type.

The main body of the paper is organized into six sections that develop the preceding ar-

gument in greater precision and generality. We start in Sections 2 and 3 by analyzing a strict

forward-looking Taylor rule in a stripped-down model that assumes perfect wage flexibility,

2 It should be noted that the estimates in Ilzetzki and Vegh (2008) are based on quarterly data.3 The entire second half of a book published by the World Bank (Perry et al., 2008a) is devoted to the "anti-investment bias of fiscal discipline" in Latin America.4 When discussing fiscal adjustment in Sub-Saharan Africa in the 1990s, Perry et al. (2008, p.19) write: "Closerinspection shows that this fiscal correction was fully attributable to a contraction of public infrastructure investment."See also the account in King (2001) of how increased debt service affected infrastructure investment in Jamaica.

2

a fixed capital stock, and a balanced budget. The stripped-down model simplifies the alge-

bra enough to permit the derivation of clean analytical results. We demonstrate specifically

that the equilibrium ceases to be saddle-point stable when either the return on infrastruc-

ture or infrastructure’s share of fiscal adjustment (ISFA) exceeds a critical threshold level.

For standard parameter values, the threshold return on infrastructure is comparatively low.

In our benchmark calibration, for example, it ranges from 7% to 19% when user fees cover

recurrent costs of infrastructure maintenance and cuts in infrastructure investment shoulder

60 - 80% of total fiscal adjustment. By contrast, most empirical estimates of the return on

infrastructure in LDCs fall somewhere between 15% and 60%.

While the analysis in Section 3 conveys useful insights, the generality of the results is

open to doubt. Several objections can be raised to the compromises required by pen-and-

paper theory: (i) other interest rate rules are often more conducive to determinacy than the

strict forward-looking Taylor rule; (ii) debt targeting, which affords policy makers substantial

flexibility in the path of fiscal adjustment, may yield results different from a balanced-budget

rule when taxes or expenditure cuts are distortionary; (iii) the simplified model abstracts

from temporary wage rigidity and private capital accumulation, features known to affect

stability and uniqueness of the equilibrium path.

Sections 4 - 7 remedy these shortcomings. We evaluate strict and flexible variants of

forward-looking and contemporaneous rules in models that incorporate private investment,

gradual clearing of the labor market, and either debt targeting or a balanced-budget rule.

Many of the results in Section 3 carry over, but some things change, most notably the

conclusion that induced cuts in infrastructure investment always undermine stability. Below

we summarize our principle findings and how they relate to the existing literature:

• The interaction between capital accumulation, infrastructure investment, and determi-nacy. Allowing for private capital accumulation greatly increases the likelihood of sunspotequilibria under a strict forward-looking Taylor rule. Dupor (2001), Carlstrom and Fuerst(2005), and Kurozumi and Van Zandweghe (2008) show that the determinacy region isvirtually empty in models that ignore adjustment costs to changing the capital stock.Inclusion of adjustment costs improves the prospects for success, but the Taylor rule re-mains problematic: indeterminacy prevails once the q-elasticity of investment is on theorder of unity or larger (Buffi e, 2014).

The results in Section 3 suggest that the fiscal effect on infrastructure investmentwill shrink the determinacy region even more, making a bad problem worse. This is not

3

the case, however, for the impact depends on the section of the determinacy region underexamination. Discouragingly, the threshold ISFA/return on infrastructure is exactly thesame as in the model with a fixed capital stock. The counterbalancing good news is thatbelow the threshold the q-elasticity compatible with determinacy increases strongly withISFA, rising in the base case from .76 in the canonical IT model (ISFA = 0) to 8 justbefore the threshold is breached (at ISFA = .54). The result is unexpected but not coun-terintuitive. Because output is demand determined in New Keynesian models, decreasesin the stock of infrastructure raise the demand for private capital. Ceteris paribus, there-fore, private investment contracts less, reducing the risk that higher real interest rates willlead to large decreases in the capital stock and large increases in future marginal coststhat drive up inflation today. The simple corollary is that determinacy holds at muchhigher values of the q-elasticity as long as ISFA remains below its destabilizing thresholdvalue.

• Temporary wage rigidity, interest rate smoothing, and strict vs.flexible IT. There areseveral ways to restore determinacy in the canonical IT model with capital accumulation.For the forward-looking Taylor rule, the literature offers three choices: (i) introduce asmall degree of temporary real wage rigidity (Buffi e, 2013, 2014); (ii) target real outputin addition to inflation (Gali et al., 2004; Huang and Meng, 2007; Kurozumi and VanZandweghe, 2008); (iii) smooth the path of the interest rate (Bullard and Mitra, 2007;Kurozumi and Van Zandweghe, 2008). Unfortunately, none of these fixes work whenthe IT regime outsources a large share of fiscal adjustment to cuts in infrastructureinvestment. All of the fixes secure large increases in the determinacy regionbelow thethreshold return (threshold ISFA) at which the equilibrium becomes indeterminate orunstable.5 But the threshold return with interest rate smoothing and/or temporary wagerigidity is the same as in the benchmark model. And flexible Taylor rules are potentiallyharmful: the threshold return decreases rapidly with the coeffi cient on the output target;in fact, a coeffi cient of .5 often eliminates the possibility of a determinate equilibrium.

• Contemporaneous Taylor rules. Carlstrom and Fuerst (2005) have shown that Taylorrules that target current inflation are generally much less susceptible to indeterminacythan forward-looking rules. But again the assumption of easy fiscal adjustment throughlump-sum transfers is critical. When the central bank follows a strict or flexible con-temporaneous rule and expenditure cuts fall partly on infrastructure investment, uniqueequilibria disappear at the same threshold return as for a strict forward-looking rule.6

• Debt targeting vs. a balanced-budget rule. The existing literature contains sharply differentconclusions about how distortionary fiscal policy affects the validity of the Taylor principlein balanced-budget vs. debt-targeting rules.7 In our model, the ranking depends on thetype of IT regime and how fast fiscal policy responds to deviations of debt from its targetlevel. A balanced-budget rule strongly dominates debt targeting when the central bank

5 The determinacy region is defined by the upper bound on the q-elasticity of investment compatible with a uniqueequilibrium.6 The same result obtains in contemporaneous rules that allow for interest rate smoothing.7 Kurozumi (2005) and Benhabib and Eusepi (2005) conclude that the determinacy region is very small for bothrules, but Linneman (2006) finds it is much larger under a debt-targeting rule.

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subscribes to strict forward-looking or contemporaneous IT. The ranking may, however,favor debt targeting when the interest rate rule targets both output and inflation. Thequalifiermay is needed because flexible IT with debt targeting dominates balanced-budgetstrict and flexible IT only if fiscal adjustment is suffi ciently fast and only if the centralbank chooses the right coeffi cient on output in the interest rate rule.8 Moreover, satisfyingthese conditions ensures only that flexible IT with debt targeting maximizes the size ofthe determinacy region, not that the determinacy region is always large; indeterminacyremains a serious threat in many cases.

At a more general level, our paper is part of a small literature that investigates how

distortionary fiscal policy affects the validity of the Taylor principle. Roisland (2003) and

Edge and Rudd (2007) show that determinacy requires the lower bound on the Taylor

coeffi cient (the coeffi cient on inflation in the interest rate rule) to exceed unity when nominal

interest income is taxed. The increase in the lower bound ensures that the after-tax real

interest rate rises in response to higher inflation. In Kurozumi (2005), Benhabib and Eusepi

(2005), and Linneman (2006), labor supply decreases and marginal cost rises as income taxes

adjust to balance the budget. This "public finance channel" dominates the conventional

demand channel for small increases in the real interest rate, leading to a tight upper bound

on the Taylor coeffi cient in strict contemporaneous and forward-looking interest rate rules.9

The indeterminacy problem disappears, however, in flexible rules that target real output

with a small positive coeffi cient.10

The most important difference between these results and ours’is that the threat to the

Taylor principle is manageable. Determinacy can be recovered either through a modest

increase in the lower bound on the Taylor coeffi cient or by targeting real output in addition

to inflation. By contrast, there is no easy solution when fiscal adjustment relies too heavily on

cuts in infrastructure investment. Some standard fixes are ineffective or counterproductive;

others are highly unreliable (debt-targeting with flexible IT). The bottom line is simple and

discomfiting: absent fiscal reform, IT is a risky proposition for LDCs.

8 It is also critical that the fiscal rule target the ratio of debt to cyclically-adjusted output, not the ratio of debtto current output. See the analysis in Section 7.3.9 This refers to the results under a balanced budget rule. With debt targeting, the tight upper bound is greatlyrelaxed and active policy ensures a unique equilibrium provided (i) lump-sum transfers absorb variations in theinflation tax and (ii) the income tax does not react too strongly to debt (Linneman, 2006).10 The results for the debt-targeting case are different in Benhabib and Eusepi (2005). The requisite coeffi cienton output in the interest rate rule is an increasing function of the coeffi cient linking the income tax to deviationsof debt from its target level. Hence if the response of the interest rate to output is too weak, the equilibrium isindeterminate.

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2. A Simple Stripped-Down Model

Throughout we work with deterministic NewKeynesian models in which prices are sticky and

firms produce differentiated goods indexed by j ∈ [0, 1]. The usual notational conventions

apply: P , M , mt = Mt/Pt−1, B, bt = Bt/Pt−1, w, K, R, and π denote the price level,

the nominal and real money supply, nominal and real holdings of bonds, the real wage, the

capital stock, the gross nominal interest rate, and the gross inflation rate.

In this section the capital stock is fixed, fiscal policy adjusts to balance the budget, and

the real wage is perfectly flexible. These strong assumptions keep the model analytically

tractable. They will be relaxed in Sections 4 and 8 when we develop more general models.

Households

All households have a utility function of the form

U =∞∑t=0

βt

[C

1−1/τt

1− 1/τ− a2

L1+1/ψs,t

1 + 1/ψ

](1)

where

C =

[∫ 1

0

c(ε−1)/εj dj

]ε/(ε−1)

,

cj is consumption of good j; β is the discount factor; Ls is labor supply; τ is the intertemporal

elasticity of substitution; ε is the elasticity of substitution between differentiated consumer

goods; and ψ is the Frisch elasticity of labor supply.

The representative agent solves a two-stage optimization problem. In the first stage, the

cj are chosen to minimize the cost of purchasing the composite consumption good C. This

yields the demand functions

cj =(pjP

)−εC (2)

and the solution for the exact consumer price index

P =

[∫ 1

0

p1−εj dj

] 11−ε

. (3)

In the second stage, the agent chooses Ct, Ls,t, and bt+1 to maximize (1) subject to the

budget constraint

bt+1 + (1 + v)Ct = wtLs,t + rK,tKt + nt +Rt−1bt/πt, (4)

6

where v is the consumption VAT; rK is the real capital rental; and n is the sum of lump-sum

transfers and rebated monopoly profits.11 On an optimal path, consumption is governed by

the Euler equation

C−1/τt = βC

−1/τt+1 Rt/πt+1 (5)

and the marginal rate of substitution between leisure and consumption equals the real wage

a2L1/ψs,t = C

−1/τt wt/(1 + v). (6)

Firms

Firms hire capital and labor in economy-wide markets. The production function for each

differentiated good is Qj = ZηG(Lj, Kj), where η > 0 and Z is the stock of infrastructure.

Assuming G(·) is homogeneous of degree one, the firm’s unit cost function is

F (wt, rK,t, Zt) = f(wt, rK,t)/Zη (7)

and

Lj,t =fw(wt, rK,t)

Zηt

Qj,t, (8)

Kj =fr(wt, rK,t)

Zηt

Qj,t. (9)

There are two sources of demand for firm output: private consumption and public in-

frastructure investment. The composite investment good Iz is assembled in the same way

as the composite consumption good. Parallel to (2), new orders for investment good j are

Izj,t = (pj,t/Pt)−εIz,t. (10)

Thus

Qj,t = (pj,t/Pt)−ε(Ct + Iz,t). (11)

Following Calvo (1983), prices change when firms receive an informative signal about the

state of the market. Each period a fraction 1 − ω of firms receive the requisite signal andadjust their price so as to maximize the present discounted value of real profits. This gives

rise to the New Keynesian Phillips Curve

πt = βπt+1 + κFt, (12)

11 User fees, which appear later in the government budget constraint, are subtracted from monopoly profits.

7

where a circumflex indicates a percentage deviation from the steady state and κ ≡ (1 −ωβ)(1− ω)/ω. As usual, the path of inflation is driven by the path of real marginal cost.

Monetary Policy

Until Section 7, the central bank targets zero inflation through the pure forward-looking

rule

Rt = παt+1/β, (13)

where α > 1 when monetary policy abides by the Taylor principle.

Coordination of Fiscal and Monetary Policy

There are two types of lump-sum transfers, T1 and T2. To simplify the algebra and justify

the use of a cashless model, we assume that T2 continuously offsets revenue from the inflation

tax net of real interest payments on government debt. The balanced-budget rule thus reads

Iz,t + T1,t = vCt + µδZt (14)

where δ is the depreciation rate and µ is the ratio of user fees to recurrent costs (i.e., depre-

ciation allowances) per unit of infrastructure. The consumption tax v and the user fee µ are

fixed, so the spending variables Iz and T1 adjust to satisfy the government budget constraint.

A fraction x of fiscal adjustment is allocated to cuts in infrastructure investment:

Iz,t = x[v(C/Iz)Ct + µZt]. (15)

Market-Clearing Conditions

Perfectly flexible factor prices ensure that demand equals supply in the markets for capital

and labor. After summing over firm demands in (8) - (9) and substituting for Qj from (11),

we have

Ls,t =fw(wt, rK,t)

Zηt

[∫ 1

0

(pj,t/Pt)−ε]

(C + Iz,t), (16)

K =fr(wt, rK,t)

Zηt

[∫ 1

0

(pj,t/Pt)−ε]

(Ct + Iz,t). (17)

Infrastructure Accumulation

The stock of infrastructure varies over time according to

Zt+1 = Iz,t + (1− δ)Zt. (18)

8

2.1 Comments on the Model

Three aspects of the model merit comment. First, an unusual variable, infrastructure user

fees, plays an important role in determining the compatibility of fiscal and monetary policy.

Governments charge various fees for the services provided by infrastructure assets: house-

holds and firms pay tariffs for electricity, water, sanitation, and irrigation; importers and

exporters pay port and cargo handling fees; revenue from tolls, gasoline taxes and vehicle

license fees increases with the size of the road network, etc. The variable µ in the model

equals the fraction of outlays on infrastructure maintenance (simply depreciation costs) cov-

ered by user fees. Cuts in infrastructure investment reduce the fiscal deficit dollar-for-dollar

in the short run. The long-run fiscal saving, however, is the original investment cut scaled

down by 1 − µ. If µ equals unity, the decrease in revenue from user fees eventually fully

offsets the decrease in capital expenditure.

The other two comments pertain to the type of fiscal adjustment that underpins the IT

regime. Lump-sum transfers, user fees, and the consumption VAT are all candidates for

the other fiscal variable that adjusts together with infrastructure investment to balance the

budget. Our choice of lump-sum transfers is motivated partly by the empirical evidence

and partly by the desire for a clean comparison with results in the existing literature. The

consensus among informed observers is that the burden of fiscal adjustment falls almost

entirely on current expenditure and public investment in the short run. The IMF (2004)

survey emphasizes the diffi culty of mobilizing revenue at business cycle frequencies; in a

similar vein, Perry et al. (2008b, p.8) note that in Latin America "the lead times required

for their approval by legislatures, and the lags between enacted legal changes and their effects

on actual revenues, make discretionary tax policy largely ineffective for cyclical stabilization

purposes." There is still a question of how to model cuts in current expenditure. From

an analytical standpoint, the advantage of equating cuts in current expenditure with cuts

in transfers is that the difference between our results and those in the existing literature

then reflects solely the impact of induced cuts in infrastructure investment. Moreover, as

will become apparent in later sections, this is where all the action takes place. We have

analyzed variants of the model in which increases in the consumption VAT replace cuts in

transfers. The results change very little. In the base case, for example, the threshold return

9

on infrastructure compatible with determinacy decreases by less than one percentage point

when infrastructure’s share of fiscal adjustment is 50% or more.

Finally, the central bank’s interest rate rule may be paired either with a debt-targeting

rule or a balanced budget rule. Following common practice in the literature, we decided to

analyze both rules. Empirically, debt-targeting and strict balanced-budget rules (i.e., rules

that do not allow for cyclical conditions) are equally prevalent among LDCs (Perry et al.,

2008b; Schaechter et al., 2012; Berganza, 2012).12 Governments may, of course, suspend or

violate "fiscal responsibility laws" in the face of sharp economic downturns. But the data

argue that this is more the exception than the rule. The general pattern in Latin America

is that expenditure declines in tandem with revenues (Perry et al., 2008b; Sturzenegger and

Werneck, 2008); consistent with this stylized fact, numerous empirical estimates find that

the fiscal deficit is either acyclical or weakly countercyclical (Gavin et al., 1996; Gavin and

Perotti, 1997; Perry, 2008; Berganza, 2012). Comparable estimates do not exist for LDCs

in other regions. The pervasive rigidity of tax rates (in the short run) and the finding of

extreme procyclicality of government expenditure in large panel datasets suggest, however,

that acyclical fiscal deficits also predominate outside of Latin America.13

3. Solving for the Equilibrium Path

The economy’s equilibrium path is controlled by three first-order difference equations in C,

π, and Z. To get the system in the right form we need to link the path of real marginal cost

F to the paths of these variables. Working toward this end, note from (6), (7), (11), (16),

and (17) that14

Ft = θLwt + θK rK,t − ηZt, (19)

(ψ + σθK)wt =

(C

Q+ψ

τ

)Ct +

δZ

QIz,t + σθK rK,t − ηZt, (20)

12 The rationale for not allowing cyclical conditions to affect the limit on the fiscal deficit is that removing discretionenhances fiscal discipline and credibility.13 See Kaminsky et al., 2004; Talvi and Vegh, 2005; Ilzetski and Vegh, 2008; Thornton, 2008; Lledo et al., 2011;and Dessus and Varoudakis, 2013.14 The Allen-Uzawa partial elasticity of substitution between factors i and j is σij = FijF/FiFj . This formula andthe adding-up conditions σLKθK + σLLθL = σKLθL + σKKθK = 0 give the solutions stated in equations (20) and(21) (where σ corresponds to σLK).

10

rK,t = wt +C

QCt +

δZ

QIz,t −

η

σθLZ, (21)

where Q is aggregate output; θi is the cost share of factor i; and σ is the elasticity of

substitution between capital and labor. Substituting for Iz in (20) and (21), and then for

rK and w in (19) produces

Ft = e1Ct + e2Zt, (22)

where

e1 ≡C

QθL

(1

ψ+θKσ

)1 + xv) +

1

τ,

e2 ≡xµδZ

QθL

(1

ψ+θKσ

)− η

θL

(θL +

1

ψ+θKσ

).

Equations (15) and (22) are the key inputs required to solve the system. Linearizing (5),

(12), and (18) now leads toCt+1

πt+1

Zt+1

=

1− τ(α− 1)κe1/β τ(α− 1)/β −τ(α− 1)κe2/β

−κe1/β 1/β −κe2/β

xvC/Z 0 1− δ(1− xµ)

Ct

πt

Zt

. (23)

Z is a state variable and C and π are jump variables. The equilibrium is a saddle point

therefore iff one of the system’s three eigenvalues lies inside the unit circle.

3.1 Fiscal Adjustment, Stability, and Uniqueness of Equilibrium

When expenditure cuts fall entirely on lump-sum transfers (x = 0), we get the signature

result in the literature that active policy (α > 1) is necessary and suffi cient for determinacy,

subject to the qualification that α not exceed a very larger upper bound.

Problems arise, however, in the more realistic case where transfers and infrastructure

investment share the burden of fiscal adjustment. The prospects for determinacy turn

on the values of two variables, x, the share of infrastructure cuts in fiscal adjustment,

and Rz, the return on infrastructure net of depreciation. In Appendix A available at

http://mypage.iu.edu/~ebuffi e, we prove

11

Proposition 1 The equilibrium is either unstable or indeterminate when

(i) 1 < α < 1 +2(1 + β)θL

κ[τ(C/Q)(1/ψ + θK/σ) + θL + τxv(C/Q)S]

and either

(ii) Rz > R∗z ≡δ

xv(θL + 1/ψ + θK/σ)[(1− xµ)N − xvθL] ,

or, equivalently,

(iii) x > x∗ ≡ δN

v[θL +Rz(θL + 1/ψ + θK/σ] + δNµ,

where

S ≡ Rz(θL + 1/ψ + θK/σ) + 2(1/ψ + θK/σ) + δθL2− δ(1− xµ)

,

N ≡ 1/ψ + θK/σ +QθL/Cτ.

The threshold return on infrastructure R∗z and the threshold value of infrastructure’s shareof fiscal adjustment (ISFA) x∗ are (a) decreasing in the user fee charged for infrastructureservices (µ), the consumption VAT (v), and the intertemporal elasticity of substitution (τ),and (b) independent of the degree of price stickiness. Furthermore, R∗z is decreasing in x,and x∗ is decreasing in Rz.

Corollary 1 The equilibrium is either indeterminate or unstable when xµ ≥ 1, Rz ≥ 0,and the central bank abides by the Taylor principle.

Remark 1 In hundreds of numerical solutions that cover all of the potentially relevantparameter space, the equilibrium is unique when Rz < R∗z and α satisfies condition (i). Wecannot prove analytically that condition (i) and Rz < R∗z are necessary and suffi cient fordeterminacy, but the perfect robustness of the numerical results qualify as a "virtual proof"(to use a term coined by Ken Judd).

Proposition 1 is a straightforward counting-on-fingers-and-toes result. To break down the

result, write condition (iii) as

x δµN + v [θL +Rz (θL + 1/ψ + θK/σ)]︸ ︷︷ ︸E2+E3

> δN︸︷︷︸E1

.

12

The threshold values R∗z and x∗ stem from the interplay of three distinct effects that deter-

mine the impact of higher interest rates on marginal cost (MC) and inflation:

Effect 1 (E1) = R ↑−→ C ↓−→ Current MC ↓−→ π ↓

Effect 2 (E2) = R ↑−→ vC ↓ and Iz ↓−→ Current MC ↓−→ π ↓

Effect 3 (E3) = R ↑−→ vC ↓ and Iz ↓−→ Z ↓−→ Future MC ↑︸ ︷︷ ︸Depends on Rz

−→ π ↑

E2+ E3 = R ↑−→ Iz ↓−→ Z ↓−→ Present value of MC ↑−→ π ↑ .

Two effects pull in the right direction. E1 is the standard effect that rules out sunspot

equilibria: arbitrary expectations of higher inflation cannot be self-fulfilling because they

trigger increases in the real interest rate that lower consumption demand; when real output

and current marginal cost decline, firms lower inflation, invalidating the original expectation.

E2 reinforces E1: at the same time that consumption falls, the central government cuts

infrastructure investment to help offset the loss in tax revenues and the cost of higher

interest payments on the internal debt. Thus current output and current marginal cost

decrease more than in the canonical IT model. But lower investment in the short run

maps into a smaller stock of infrastructure and higher marginal costs in the future. The

magnitude of this third effect (E3) depends on the real return on infrastructure. Crucially,

the combined effect E2 + E3 is positive and increasing in Rz and x. Determinacy gives way

to indeterminacy/instability therefore when Rz or x is large enough that E2 + E3 dominates

E1 (see Figure 1). Since the E2 + E3 effect is bigger the bigger the ex ante fiscal deficit and

the bigger the induced cut in infrastructure investment, R∗z is a decreasing function of µ, v,

x, and τ .15

Corollary 1 is a byproduct of Proposition 1 but an altogether different type of result.

Obviously it does not rely on a powerful E3 effect. Rather it states a simple condition

under which unstable feedback effects between changes in the stock of infrastructure and

infrastructure investment render IT inoperable. Return to the law of motion Zt+1 = Iz,t−δZt.A decrease in Z reduces Iz by xµδdZ through the rule for fiscal adjustment. The amount

15 R∗z/x∗ decreases with τ because the increase in the real interest rate reduces consumption and VAT revenue more

when the intertemporal elasticity of substitution is high.

13

of investment needed to maintain the infrastructure stock decreases by δdZ. Consequently,

when xµ > 1 the Iz-Z feedback loop does not converge.

3.1.1 How Big Are R∗z and x∗?

A full, proper answer to this question awaits the results in Sections 5 and 7. Nevertheless,

it is already evident that IT skates on thin ice in the empirically relevant parameter space.

Corollary 1 tells us that R∗z can be very small– zero– in countries where user fees are a

multiple of recurrent costs. This group is a small minority, but R∗z is often dangerously

low even when fees fail to cover recurrent costs. Suppose, for example, that µ = .75,

τ = σ = ψ = 1, θL = .67, and δ = .0125 (quarterly depreciation rate). The threshold

return is then 22 - 30% for x = .5 - .6 and 11 - 16% for x = .7 - .8. These numbers are large

in absolute terms but well below most empirical estimates of Rz in LDCs.16

To repeat, however, we do not wish to claim too much at this stage. Proposition 1 is

suggestive, not fully convincing. The underlying model is very simple and the analysis is con-

fined to the strict forward-looking Taylor rule – the rule most vulnerable to indeterminacy.

Building a stronger case entails therefore analysis of more Taylor rules in a more complete

model. This is supplied in the next four sections. Previewing the bottom line, some results

change, but, overall, the predictions of Proposition 1 hold up remarkably well.17

4. The Full-Blown Model

Our preferred model incorporates capital accumulation, money, and temporary real wage

rigidity. A cash model is not essential at this stage. It is required, however, for an exact

comparison of the solutions for the balanced-budget and debt-targeting rules. In the stan-

dard setup, money can be safely ignored because fiscal adjustment via lump-sum transfers

does not affect the economy’s equilibrium path. But when some of the instruments of fiscal

16 See Table 1 in Buffi e et al. (2014) for a summary of empirical estimates of Rz in LDCs. In seventeen of thirty-twoestimates, the return equals or exceeds 30%. The average return is 34.1%.17 The upper bound on α in Proposition 1 is decreasing in x. A slightly less stripped-down model argues, however,that there is a strong presumption the upper bound increases with x. When the increase in interest payments on thedebt enters the rule that determines cuts in Iz, R∗z is the same as in Proposition 1 but the term involving x in thedenominator of the upper bound on α changes to (τv − 2Rb/C)x(C/Q)S. The upper bound increases with x when2Rb/C > τv – a condition that is virtually certain to hold. (τ < 1, v = .1 - .2, while the ratio of debt to quarterlyconsumption is at least .4.) This foreshadows the result in the more general model that for Rz < R∗z the determinacyregion is larger than in the canonical IT model.

14

adjustment are distortionary, the money demand equation is not irrelevant: it has to be

consulted in the solution for debt-targeting to track how open market operations alter the

stock of debt and the total amount of fiscal adjustment associated with IT.

Since the equations in the stripped-down model carry over directly or with slight modi-

fications, we present the new model quickly with a minimum of commentary.

Households

The representative agent solves

Max

∞∑t=0

βt

[C

1−1/τt

1− 1/τ+ a1

m1−1/τt+1

1− 1/τ− a2

L1+1/ψs,t

1 + 1/ψ

](24)

subject to

bt+1 +mt+1 + (1 + v)Ct + It +g

2

(ItKt

− δ)2

Kt = wtLs,t + rK,tKt +mt/πt

+nt +Rt−1bt/πt, (25)

Kt+1 = It + (1− δ)Kt (26)

where I is private investment and g(It/Kt − δ)2Kt/2 captures adjustment costs incurred

in changing the capital stock. The specification of the budget constraint assumes that the

composite private investment good is constructed in the same way as the composite goods

C and Iz.

More choice variables come with more first-order conditions. Besides (5) and (6), op-

timality requires that the marginal rate of substitution between money and consumption

equal the nominal interest rate

a1mt+1−1/τ =

C−1/τt

1 + v

(Rt − 1

Rt

)(27)

and that the capital rental net of adjustment costs and depreciation equal the real interest

rate:

Rt

πt+1

[1 + g

(ItKt

− δ)]

= rK,t+1 + 1− δ +g

2

(It+1

Kt+1

− δ)2

+ g

(It+1

Kt+1

− δ). (28)

15

Firms

Equations (7) - (10) are unchanged, while equation (11) now includes private investment

demand

Qj,t = (pj,t/Pt)−ε

[Ct + Iz,t + It +

g

2

(ItKt

− δ)2

Kt

]. (11′)

Monetary Policy and Infrastructure Accumulation

The forward-looking Taylor rule and the law of motion for the stock of infrastructure do

not change.

Coordination of Fiscal and Monetary Policy

The government budget constraint is

mt+1 + bt+1 −mt

πt= Iz,t + Tt +Rt−1

btπt− vCt − µδZt.

In keeping with commitment to run a balanced budget, the central bank holds the real stock

of domestic credit (m+ b) constant. This, the Taylor rule in (13), and (27) imply

b

mbt+1 = −mt+1 =

τα

R− 1πt+1 − Ct, (29)

Iz,t + Tt = vCt + µδZt −(Rt−1

πt− 1

)bt +

πt − 1

πtmt. (30)

The fiscal rule for adjustment of Iz now includes interest payments on the debt.18 Hence

the counterpart of (15) is

Iz,t = x

[vC

IzCt + µZt +

Rb

Iz(πt − Rt−1)− (R− 1)

b

Izbt

], (15′)

Aggregate Factor Demand and Real Wage Adjustment

Summing over firm demands in (8)-(9) and substituting for Qj from (11′) yields

Ld,t =fw(wt, rk,t)

Zηt

[∫ 1

0

(pj,t/Pt)−ε] [

Ct + Iz,t + It +g

2

(ItKt

− δ)2

Kt

], (31)

Kt =fr(wt, rk,t)

Zηt

[∫ 1

0

(pj,t/Pt)−ε][

Ct + Iz,t + It +g

2

(ItKt

− δ)2

Kt

]. (32)

Since Kt is predetermined, equation (32) is the condition for demand to equal supply in

the capital market. In the labor market, we assume the real wage adjusts gradually in the

18 Lump-sum taxes offset variation in revenue from the inflation tax. Incorporating the inflation tax into theadjustment rule for Iz does not change any of the results presented later in Table 2.

16

direction of its market-clearing level. Following Blanchard and Gali (2007),

wt − wt−1

wt−1

= hLd,t − Ls,t

Ls,t, h > 0, (33)

st = wt−1, (34)

where the parameter h reflects the weight of outstanding contracts and the state variable s

tracks the inertial component of wage adjustment.

Although our analysis focuses mainly on the flex-wage case, a flex-wage, full-employment

model is too restrictive for the issue at hand. Temporary real wage rigidity greatly enhances

the prospects for determinacy in the standard setup that offl oads all fiscal adjustment onto

lump-sum transfers (Buffi e, 2014).19 We need to work therefore with a general specification

that can be finely calibrated to different speeds of adjustment in the labor market. Equation

(33) meets this criterion: it can accomodate any degree of real wage flexibility, including the

polar cases of completely rigid (h = 0) and perfectly flexible (h =∞) wages.

4.1 Model Calibration

The core dynamic system consists of eight first-order equations in C, I, K, s, Z, R, b, and π.

K, s, R, b, and Z are state variables, so saddle-point stability requires five eigenvalues inside

the unit circle. (The log-linearized solution for the core system is derived in the Appendix

B at http://mypage.iu.edu/~ebuffi e.)

Table 1 lists the parameter values for the benchmark calibration of the model and the

range of values examined in sensitivity tests. We set the time period at one quarter and

assigned ordinary values to the elasticity of substitution between differentiated varieties

(ε = 6), the coeffi cient on inflation in the Taylor rule (α = 1.5), the depreciation rate

(δ = .0125), and the Calvo sticky-price parameter (ω = .75). The values for all other

parameters are based on hard data or empirical estimates for LDCs. With respect to the

fiscal variables:

• Ratio of government debt to GDP. Twenty-five percent is representative of the ratio ofdomestic debt to GDP outside of the poorest LDCs (many of which do not practice IT).In emerging market economies, the internal public debt is approximately 30% of GDP(IMF, 2003); for LDCs overall, the average is 23% (Panizza, 2008).

19 The empirical evidence for real wage rigidity is extensive and fully on par with that for nominal wage rigidity.See Buffi e (2014).

17

• Consumption VAT (v). The consumption VAT in the model proxies for all indirect taxrates. At 20%, it is slightly higher than the average VAT in Sub-Saharan Africa andLatin America (IMF, 2010).

• Initial ratio of infrastructure investment to GDP. Outlays on operations and maintenance(O+M) of infrastructure average 3.3% of GDP in Sub-Saharan Africa. But true O+Mcosts are 40-50% higher (Briceno-Garmendia et al., 2008). Lacking data for other parts ofthe Third World, we took the African data as a guide and set infrastructure investmentequal to 5% of GDP.

• Ratio of user fees to recurrent costs per unit of infrastructure (µ). There is tremendousvariation in user fees across countries and types of infrastructure. Our choice of .75 forµ is a guesstimate based on the data for Sub-Saharan Africa in Briceno-Garmendia etal. (2008) and on the average user fees reported in the World Bank (1994b).

5. Numerical Results

New Keynesian models with capital accumulation and a pure forward-looking Taylor rule

suffer from indeterminacy when the q-elasticity of private investment spending exceeds a

critical threshold value. For plausible parameter values, the threshold value lies between

.5 and 1.5 (Buffi e, 2014), a range that brackets the majority of empirical estimates of the

q-elasticity for developed countries.

In our model induced cuts in infrastructure investment are a second potential source of

indeterminacy/instability. This complicates the analysis as the interactions of three key

variables, the return on infrastructure (Rz), infrastructure’s share of fiscal adjustment (x),

and the q-elasticity of private investment (Ω), jointly circumscribe the set of determinate

equilibria. Going forward, our strategy is to piece together a three-dimensional map of the

determinacy region by charting boundary lines in the Rz-x plane and the Ω-x plane.

5.1 The Threshold Return on Infrastructure (R∗z)

The analysis in this section is in the spirit of Proposition 1. We fix Ω at unity and compute

the threshold value of Rz for different values of x. (Rz is stated as the annual, not quarterly,

return.)

Table 2 shows the outcome in the flex-wage, full-employment model. Consistent with

Proposition 1, R∗z is strongly decreasing in x and µ but invariant to the initial level of

debt and the degree of price stickiness. It is moderately sensitive to τ , ψ, θL, σ, and β.

18

Importantly, however, the threshold return is below 25% in 81% of the runs for x = .5 - .8.

Thus, if empirical estimates of Rz are correct, many countries occupy points outside the

determinacy frontier. The obvious implication for policy is that LDCs should take it slow,

transitioning to full-fledged IT only after reforms enhance fiscal flexibility (reducing x) or

after a period of high public investment reduces the scarcity of infrastructure (lowering Rz).

These troubling results are largely independent of the value assumed for the q-elasticity of

investment. Naturally the equilibrium is always indeterminate above some threshold value

Ω∗. But for 0 < Ω < Ω∗, the threshold value of Rz is exactly the same. In light of what

follows, we hasten to add that the absence of causal influence in one direction does not rule

out influence in the opposite direction. As will become apparent shortly, although variations

in Ω below Ω∗ do not affect R∗z/x∗, variations in Rz/x below R∗z/x

∗ do affect Ω∗. What’s

more, the effect is large.

5.2 The Threshold Value of Ω

The second way to slice the determinacy region is to fix Rz (x) and investigate how the

threshold value of Ω varies with x (Rz). This demarcation tells us whether the determi-

nacy region is larger or smaller for values of x that do not preclude existence of a unique

equilibrium.

Figure 2 does not equivocate: the prospects for determinacy are much, much better until

x reaches x∗. (For x ≥ x∗, the equilibrium is always indeterminate or unstable.) The

canonical IT model assumes x = 0. In this case, the equilibrium becomes indeterminate

once the q-elasticity exceeds .76. But the outlook improves dramatically as x increases: Ω∗

rises to 4.71 at x = .30 and to 8 just short of the discontinuity at x∗ = .543.

On first acquaintance, the result in Figure 2 seems paradoxical. It builds logically, how-

ever, on previous results. Recall the three effects that determine the impact of lower con-

sumption and cuts in infrastructure investment on the present value of marginal costs and

19

current inflation:20

Effect 1 (E1) = R ↑−→ C ↓−→ Current MC ↓−→ π ↓

Effect 2 (E2) = R ↑−→ vC ↓ and Rb ↑ −→ Iz ↓−→ Current MC ↓−→ π ↓

Effect 3 (E3) = R ↑−→ vC ↓ and Rb ↑ −→ Iz ↓−→ Z ↓−→ Future MC ↑︸ ︷︷ ︸Depends on Rz

−→ π ↑

E2+ E3 = R ↑−→ Iz ↓−→ Z ↓−→ Present value of MC ↑−→ π ↑ .

Private investment and capital accumulation add two more effects:

Effect 4 (E4) = R ↑−→ I ↓−→ Current MC ↓−→ π ↓

Effect 5 (E5) = R ↑−→ I ↓−→K ↓−→ Future MC ↑−→ π ↑

E4 + E5 = R ↑−→ I ↓ andK ↓︸ ︷︷ ︸Size depends on Ω

−→ Present value of MC ↑−→ π ↑

The combined E4 + E5 effect is positive and increasing in Ω. This relationship is depicted

in the second quadrant of Figure 4. The other two schedules import the content of Figure

1 in Section 3.1. Points on the downward-sloping schedule in the first quadrant equal the

vertical distance between the solid and dashed lines in the fourth quadrant; hence —(E1 +

E2 + E3) decreases monotonically with x, hitting zero at x∗.

In the canonical IT model, x = 0 and the equilibrium is indeterminate for Ω > Ω0. When

x > 0, the E2 + E3 effect enters the picture. Ceteris paribus, this reduces the threshold

value of Ω. But other things are not equal, for private investment decreases less, weakening

the E4 + E5 effect. After cuts in Iz take their toll on Z, both the real capital rental and

the real wage rise because firms need more capital and more labor to produce the demand-

determined level of output. The direct effect on the demand for capital bids up the capital

rental by rK = −(η/θLσ)Z, where η = (Rz + δ)Z/Q is the elasticity of output with respect

to the stock of infrastructure.21 In the benchmark calibration, substitution effects induced

by a higher wage (w ↑−→ rK ↑) magnify the direct effect three-fold. Future capital rentalsare much higher therefore when x > 0 and IT is accompanied by cuts in Iz. Formally (see

20 Nominal interest payments are predetermined in the discrete-time model. The increase in Rb in Effects 2 and 3occurs with a one period lag.21 The direct effect is derived from (32), with real wage and real output held constant.

20

the Appendix),22

rK = −(Rz + δ)Z

QθLσ︸ ︷︷ ︸Direct effect

×(

1 +σ

ψ

)︸ ︷︷ ︸3 in base case

Z. (35)

Since Tobin’s q depends on the entire future path of the capital rental, private investment de-

creases less for any given Ω, causing the E4 + E5 schedule to pivot left (Figure 4). Moreover,

this effect dominates the movement down the —(E1 + E2 + E3) schedule. Consequently,

Ω∗ increases rapidly with x right up to x∗. At x∗, E1 + E2 + E3 changes sign, creating

a massive discontinuity. The equilibrium must be indeterminate or unstable for x ≥ x∗

because E1 + E2 + E3 cannot possibly offset E4 + E5 – both effects are positive.

If the above explanation is correct, then the equilibrium path following a cost-push shock

should show a smaller decrease in private investment and a smaller increase in inflation for

x > 0 than for x = 0.23 Impulse responses (available upon request) confirm both predictions.

5.3 Temporary Wage Rigidity

Temporary wage rigidity substantially resolves the indeterminacy problem in the canonical

IT model (Buffi e, 2013, 2014). This result shows up in Figure 4 in the jump of the vertical

intercept from .76 to 21.5. The cure works in the same way when some expenditure cuts fall

on infrastructure investment, but only up to a point. The rigid logic of Figure 3 continues

to apply. Temporary wage rigidity makes the E4 + E5 schedule flatter in slope for all x,

but it does not shift the point of discontinuity. IT still breaks down for x ≥ x∗.

6. Alternative Taylor Rules

Pure forward-looking Taylor rules are highly susceptible to sunspot equilibria in New Key-

nesian models with capital accumulation. This is not true, however, of other Taylor rules.

Uniqueness is virtually guaranteed in a pure contemporaneous rule (Carlstrom and Fuerst,

2005) and in forward-looking rules that target real output (Gali et al., 2004; Huang and

Meng, 2007; Kurozumi and Van Zandweghe, 2008) or that smooth the path of the interest

22 The solution holds real output constant.23 Ω∗ −Ω mirrors how much larger —(E1 + E2 + E3) is than E4 + E5. Since Ω∗ increases with x, inflation shouldincrease less the larger is x.

21

rate (Bullard and Mitra, 2007; Kurozumi and Van Zandweghe, 2008).24 Arguably, therefore,

indeterminacy is a problem only when the central bank chooses the wrong Taylor rule.

In the next three sections we investigate whether these fixes continue to work when

supporting fiscal adjustment entails cuts in infrastructure investment.

6.1 Flexible Forward-Looking IT

A flexible forward-looking Taylor rule targets both future inflation and current output,

viz.:25

Rt = απt+1 + χQt, χ > 0 (36)

Figures 5 - 7 reproduce the findings in the existing literature while highlighting their

limitations. Setting χ at .15 (Figures 5 and 6) effectively ensures a unique equilibrium

in the canonical IT model. (For x = 0, the threshold value of Ω jumps from .76 to 19.)

Discouragingly, however, x∗ decreases from .43 - .54 to .36 - .46. For LDCs, where x is often

dangerously high, this is a nasty tradeoff to contemplate. Certainly the central bank cannot

target real output in any meaningful sense (Figure 7); even pedestrian values of χ on the

order of .5 eliminate the possibility of a stable, unique equilibrium when the return on

infrastructure exceeds 10%.

6.2 Contemporaneous Rules

A pure contemporaneous rule (Rt = απt) strongly dominates pure and modified forward-

looking rules: the threshold value of x is the same as in the pure forward-looking rule, but

there is no upper bound on Ω for x < x∗ (Figure 8).26

6.3 Interest Rate Smoothing

Under interest rate smoothing,

Rt = α(1− φ)πt+1 + φRt−1, 0 < φ < 1, (37a)

24 The effi cacy of interest rate smoothing is sensitive, however, to the degree of price stickiness (see Kurozumi andVan Zandweghe, 2008).25 We have also analyzed a forward-looking rule that targets future output. The results are identical.26 Figure 8 also applies when the real wage is temporarily rigid. The results are invariant to the value of h inequation (33).

22

or

Rt = α(1− φ)πt + φRt−1, 0 < φ < 1, (37b)

depending on whether the central bank targets current or future inflation.

Figure 8 applies to both specifications for all values of φ; interest rate smoothing guar-

antees determinacy when x < x∗; for x > x∗, it is completely ineffective regardless of the

degree of smoothing and regardless of the choice of inflation target.

7. Debt Targeting

Balancing the budget period by period requires continuous, fast fiscal adjustment. Debt-

targeting rules are more flexible. In the short run, the government issues debt both to

implement the interest rate rule and to finance the fiscal deficit. Infrastructure investment

and transfers then adjust to bring the stock of debt back to its target level b. The government

budget constraint and the rules for fiscal adjustment are

bt+1 +mt+1 = Iz,t + Tt +Rt−1bt/πt +mt/πt − vCt − µδZt, (38)

Iz,t = Iz − xγ(bt − b), (39)

Tt = T − (1− x)γ(bt − b), (40)

where γ > 0 controls the response of total expenditure to increases in the stock of debt.

Linearizing equations (27), (38), and (39) yields

bt+1 +m

bmt+1 = −vC

bCt −

(R +

m

b

)πt − µ

δZ

bZt +RRt−1 + (R− γ)bt +

m

bmt,(38′)

Iz,t = −xγbδZ

bt, (39′)

ταπt+1 + mt+1 = Ct. (27′)

Equation (39′) replaces (15′) and mt now enters the core dynamic system as an additional

state variable. (Recall that mt ≡Mt/Pt−1.) The rest of the model is the same as in Section

4.

Under debt targeting, γ, the parameter that controls the overall speed of fiscal adjustment,

joins Rz, Ω, and x in the list of key variables that govern determinacy and stability of the

equilibrium path. For γ > R− 1, the coeffi cient on bt in (38′) is less than unity. In standard

23

models of debt targeting (e.g., Bohn, 1998), this condition is necessary and suffi cient for b

to converge to b on a unique path.27 In our model, it is only necessary, not suffi cient; as will

become apparent shortly, stability often requires γ to be several times larger than the real

interest rate.

Estimates for LDCs (Abiad and Ostry, 2005; Mendoza and Ostry, 2008) place γ between

.03 and .08 in countries with low or moderate levels of debt and between 0 and .02 in

countries with high debt. The estimates for developed countries (Bohn, 1998; Mendoza and

Ostry, 2008; Ghosh et al., 2011) fall in the same general range, with the exception of Bohn

(2005), which finds that γ might be as high as .12 in the United States. In keeping with

this evidence, we allow γ to take four values: the low value .025, the average value .05, the

high value .075, and the very high value .10.

7.1 Strict Forward-Looking IT

Placing Table 3 beside Table 2 provides a direct comparison of the threshold values of Rz

in the debt-targeting and balanced-budget rules. The upper panel of the allows the speed

of fiscal adjustment to vary from low to very high in the base case. In the lower panel, all

of the runs assume the average speed of adjustment (γ = .05).

The unmistakable message of the side-by-side comparison is that debt targeting (DT)

greatly reduces the size of the determinacy region. Every number in Table 3 is much smaller

than the corresponding number in Table 2. Consider the results for the average speed of

fiscal adjustment. For x = .3 - .6 in the base case (γ = .05 in the upper panel), R∗z is 53-85%

lower than with a balanced-budget rule (BBR); worse yet, for x ≥ .673 the equilibrium is

always unstable. In the lower panel, R∗z drops below 10% in 22 of 28 runs where x = .5 -

.6. Faster speeds of adjustment give better results, but even when γ is at the high end

of empirical estimates (γ = .10 in the upper panel), DT reduces R∗z by 6 - 12 percentage

points.28

Simple fiscal arithmetic underlies these results. DT allows the government to delay fiscal

adjustment when the central bank raises the real interest rate to combat inflation. But

the price of delay is more debt, higher interest payments on the debt, and larger total

27 γ > 0 is suffi cient for determinacy but not for convergence of b. See Bohn (1998).28 R∗z does not get within two percentage points of the solution in the BBR until γ rises to .30.

24

cuts in infrastructure investment over the adjustment cycle. Consequently, the potential

for the interest rate rule and the fiscal rule to form an unstable feedback loop is much

greater under DT than under a BBR. This conclusion differs sharply from the benign view

of DT in the existing literature. The reason is that infrastructure investment is one of the

adjusting fiscal variables. Conventional models of DT treat the primary fiscal surplus as the

adjusting "instrument."29 Policy makers then enjoy considerable flexibility in the timing of

fiscal adjustment as the stock of debt converges to its target level under the weak condition

that γ exceeds the real interest rate. In our model, however, flexibility diminishes quickly

as infrastructure’s share in expenditure cuts increases. For empirically observed values of x

and Rz (x ≥ .40, Rz ≥ .10), fiscal adjustment must be very fast to prevent instability.

7.1.1 Determinacy in the Ω -x Plane

Sunspot equilibria proliferate when the q-elasticity of investment spending exceeds the

threshold value Ω∗. Under a BBR, Ω∗ increases strongly with infrastructure’s share of fiscal

adjustment until x hits the threshold value x∗ incompatible with stability (see Figure 2).

This result carries over to DT, but with the twist that both x∗ and Ω∗ are highly sensitive

to the speed of fiscal adjustment. The value of Ω∗ for the BBR is .545. Under DT (Figures

9 and 10), x∗ decreases to .41 - .45 for γ = .075 - .10 and to .10 - .33 for γ = .025 - .05. In the

runs with low and average speeds of fiscal adjustment (γ = .025, .05), Ω∗ is also lower; thus,

DT shrinks the determinacy region in every dimension (i.e., in both the Rz -x and the Ω - x

planes). At above-average and very fast speeds of adjustment, x∗ decreases and Ω∗ increases,

creating some ambiguity. But since the data argue that x > .40 in the great majority of

LDCs, the tradeoff is unfavorable. DT still reduces the likelihood of determinacy.

The results in Table 3 and the solutions for x∗ in the Ω -x plane generalize to variants of

the model with temporary wage rigidity, interest rate smoothing, and contemporaneous IT.

It is too early, however, to conclude that DT is inferior to BBR. There is one more case to

investigate.

29 The justification for treating the primary surplus as a fiscal instrument is that the condition for "responsible"fiscal policy in DT "does not require explicit knowledge of fiscal policy rules" (Mendoza and Ostry, 2008, p.1082).Our results dispute this claim.

25

7.2 Flexible IT

Flexible IT is a double-edged sword. In some cases, it solves the indeterminacy problem; in

others, it makes the problem worse. Much depends on the speed of fiscal adjustment, policy

makers’choice of coeffi cients in the Taylor rule, the degree of price stickiness, and the values

of the intertemporal elasticity of substitution and the elasticity of labor supply.

Table 4 contains a bewildering variety of outcomes.30 Some criterion is needed to organize

and evaluate the results. Given the high estimates of x in the literature, we propose x∗ > .75

and x∗ > .50 as strong and weak tests for reliability of the policy regime.

Not surprisingly, flexible IT performs poorly when the speed of fiscal adjustment is low.

For γ = .025, the pass rates on the strong and weak tests are 6.2% and 22.3%, respectively.

The scores improve substantially when γ = .05 - .10. But while the prospects for determinacy

are quite good in the base case, low values of x∗ are common in the other panels. At the

average speed of fiscal adjustment (γ = .05), the pass rate is 45.5% on the weak test and

26.8% for the strong test. Even at high speeds of adjustment (γ = .075, .10), the pass rates

improve to only 40.2 and 60.3%.

The upshot of all this is that the propensity to adjust through cuts in infrastructure

remains a serious problem. Flexible IT with DT and fast fiscal adjustment offers the best

chance of achieving determinacy. But the best chance is far from a sure thing. Uncertainty

about the values of deep parameters and the speed of supporting fiscal adjustment creates

lots of opportunities to choose wrong. Nor is it easy to devise general guidelines for maxi-

mizing the probability of determinacy: plots of x∗ against α and χ may be upward-sloping,

downward-sloping, inverted-V shaped, N-shaped or M-shaped. There is only one robust re-

sult: since x∗ is always increasing in γ, fiscal adjustment should be as fast as socio-political

constraints allows.

7.3 An All-Important Caveat: DT Must Target the Ratio of Debtto Cyclically-Adjusted Output

The rule in equations (39) and (40) targets the ratio of debt to cyclically-adjusted output

(omitted because units are chosen so that steady-state output equals unity). This is critical.

30 Table 5 states results for x∗. Alternatively, we could generate solutions for R∗z for a given value of x. The scenariosin Table 5 that produce low values for x∗ then produce low values of R∗z .

26

Table 5 shows what happens when the government makes the mistake of targeting the ratio

of debt to current ouput. The results in the two panels should be compared with those for

µ = 0 - 1 in Table 3 and for τ = .50 (the first panel) in Table 4.

Targeting the ratio of debt to current output is disastrous when the central bank engages

in strict forward-looking IT. The problem is that the interaction of the fiscal and monetary

rules can easily lead to quick, magnified cuts in infrastructure investment. When the increase

in the real interest rate reduces real output, the debt ratio rises and the DT rule triggers

an immediate cut in infrastructure investment. The cut in infrastructure investment causes

output to contract more, which causes the debt ratio to rise more, which triggers further cuts

in infrastructure investment, etc. The feedback effects become unstable at low values of Rz,

greatly shrinking the determinacy region.31 Strict forward-looking IT combined with a fiscal

rule that targets the ratio of debt to current output amounts to a formula for instability.

The results for flexible IT are less one-sided. In some cases – especially in the runs for

α = 1.25 – U’s replace high values for x∗. Overall, however, the results are much worse.

Uniqueness is guaranteed in 29 of the 48 runs for α = 1.5 - 2 in Table 4 versus only 5 runs

in Table 5; moreover, in 38 of the other 43 runs in Table 5, the threshold value of x is below

.40. The pass rate on the weak test (in the panel for τ = .50) in Table 4 is 89%; in Table 5,

it is a woeful 33%.

8. Concluding Remarks

IT requires supporting fiscal adjustment in the right quantity and the right quality. Both

conditions are satisfied under the usual assumption that lump-sum transfers adjust to bal-

ance the budget. In LDCs, however, the costs of short- and medium-term fiscal adjustment

fall disproportionately on infrastructure investment. Given that infrastructure generally

pays a high return, the quality of supporting fiscal adjustment is problematic.

In this paper we have shown that low-quality fiscal adjustment threatens the viability of IT

in LDCs. Our central conclusion, that excessive reliance on cuts in infrastructure investment

leads to indeterminacy or, more often, instability, is depressingly robust. It holds when the

q-elasticity of private investment is large or small, when the real wage is perfectly flexible

31 This conclusion is robust to the value of γ. The threshold value of Rz is greatest for γ ≈ .05. Runs with higheror lower values of γ return lower values of R∗z .

27

or highly rigid, for low and high levels of public debt, for wide variations in the values of

deep parameters that describe preferences and technology, for balanced-budget and debt-

targeting rules, for pure and flexible variants of forward-looking and contemporaneous IT,

and for Taylor rules that incorporate interest rate smoothing. Doubtless some countries

reside in the right part of the parameter space and can adopt IT right away. But this group

is small. In most LDCs, prior investment to reduce the scarcity of infrastructure and/or

the development of additional policy instruments to reduce infrastructure’s share of fiscal

adjustment remain preconditions for adoption of IT.

28

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32

Table 1: Calibration of the model (time period = 1 quarter).

Variable/Parameter Base Case Range Ratio of money balances to quarterly GDP .40 -

Taylor coefficient (α) 1.5 -

Elasticity of substitution between differentiated varieties (ε) 6 -

Discount factor (β) .98 .97 - .99

Depreciation rate (δ) .0125 -

Ratio of government debt to quarterly GDP 1 .4 - 2

Consumption VAT (v) .20 -

Frisch elasticity of labor supply (ψ) .5 .2 - 3

Initial ratio of infrastructure investment to GDP .05 -

Ratio of user fees to recurrent costs (μ) .75 0-1

Elasticity of substitution between capital and labor (σ) 1 .5 - 1.5

Average duration of a price quote [1/(1 – ω)] 4 quarters 1.5-6 quarters

Cost share of labor (θL) .55 .40 - .72

Table 2: Threshold value of the return on infrastructure.

Scenario x = .3 x = .4 x = .5 x = .6 x = .7 x = .8 Base case1 51.4 33.9 23.4 16.4 11.4 7.6

μ = 0 67.1 49.6 39.1 32.1 27.1 23.4

μ = .25 61.8 44.4 33.9 26.9 21.9 18.1 μ = .50 56.6 39.1 28.6 21.6 16.6 12.9 μ = 1 46.1 28.6 18.1 11.2 6.2 2.4

τ = .20 93.2 62.2 43.6 31.2 22.4 15.8 τ = .75 42.0 27.6 18.9 13.1 9.0 5.8 τ = 1 37.4 24.4 16.6 11.4 7.7 5.0

ψ = .20 44.5 29.4 20.4 14.3 10.0 6.8 ψ = 1 58.2 38.4 26.4 18.5 12.8 8.6 ψ = 3 68.5 45.0 31.0 21.6 14.9 9.9

σ = .50 59.0 39.2 27.2 19.3 13.6 9.4 σ = 1.5 45.4 29.7 20.4 14.1 9.6 6.3

θL = .40 38.4 24.9 16.8 11.4 7.6 4.7 θL = .72 64.5 42.9 30.0 21.4 15.2 10.6

β = .97 48.0 31.6 21.7 15.2 10.4 6.9 β = .99 57.5 38.1 26.4 18.7 13.1 9.0

Debt /GDP2 = .4 Same as in the base case Debt/GDP2 = 2 Same as in the base case

ω = .33 Same as in the base case ω = .83 Same as in the base case

1 The q-elasticity of private investment spending equals unity. See Table 2 for other base case parameter values. 2 Ratio of debt to quarterly GDP.

Table 3: Threshold value of the return on infrastructure under debt targeting.

Base Case1 Scenario x = .3 x = .4 x = .5 x = .6 x = .7 x = .8 γ = .025 Unstable for x > .208 γ = .05 24.1 13.2 6.7 2.4 Unstable for x > .673 γ = .075 34.1 20.7 12.7 7.4 3.6 .7 γ = .10 39.1 24.5 15.7 9.9 5.7 2.6

Balanced Budget 51.4 33.9 23.4 16.4 11.4 7.6

γ = .05

Scenario x = .3 x = .4 x = .5 x = .6 x = .7 x = .8 μ = 0 40.6 29.8 23.2 18.9 15.8 13.5

μ = .25 35.1 24.2 17.7 13.4 10.3 8.0 μ = .50 29.6 18.8 12.2 7.9 4.8 2.4 μ = 1 18.6 7.7 1.2 Unstable for x > .523

τ = .20 44.9 25.7 14.1 6.4 .9 Unstable for

x >.718 τ = .75 19.5 10.5 5.1 1.5 Unstable for x > .652 τ = 1 17.2 9.1 4.2 1.0 Unstable for x > .639

ψ = .20 21.0 11.6 6.0 2.2 Unstable for x > .677 ψ = 1 27.2 14.9 7.5 2.6 Unstable for x > .668 ψ = 3 32.0 17.4 8.6 2.8 Unstable for x > .663

σ = .50 28.0 15.7 8.3 3.4 Unstable for x > .693 σ = 1.5 21.0 11.3 5.5 1.6 Unstable for x > .652

θL = .40 17.4 9.1 4.0 .7 Unstable for x > .624 θL = .72 30.8 17.4 9.4 4.0 .2 Unstable for x

> .706

β = .97 8.1 1.4 Unstable for x > .429 β = .99 43.0 27.1 17.6 11.2 6.6 3.2

Debt /GDP = .4 Same as in the base case Debt/GDP = 2 Same as in the base case

ω = .33 Same as in the base case ω = .83 Same as in the base case

1 The q-elasticity of private investment spending equals unity. See Table 2 for other base case parameter values. Debt/GDP is the ratio of debt to quarterly GDP.

Table 4: Threshold value of x in flexible IT with Debt Targeting.1

τ = .50 α = 1.25 α = 1.5 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .66 U U U .57 U U U

.50 .45 .71 .85 .96 .76 U U U

.75 .40 .62 .77 U .57 .92 U U 1 .41 .64 U U .48 .78 .94 U α = 1.75 α = 2 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .20 .64 .79 .87 .15 .48 .59 .65

.50 U U U U .57 U U U

.75 .80 U U U U U U U 1 .63 U U U .82 U U U τ = .75 α = 1.25 α = 1.5 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .43 .65 .76 .83 .64 U U U

.50 .28 .41 .48 .53 .46 .70 .82 .91

.75 .25 .36 .42 .49 .34 .52 .61 .67 1 .25 .35 .46 U .29 .43 .51 .57 α = 1.75 α = 2 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .19 .60 .74 .81 .14 .44 .54 .59

.50 .68 U U U .64 U U U

.75 .47 .72 .85 .93 .62 .93 U U 1 .38 .57 .68 .75 .47 .73 .86 .95 τ = 1 α = 1.25 α = 1.5 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .31 .45 .52 .57 .60 .84 .94 U

.50 .20 .29 .33 .36 .32 .47 .55 .60

.75 .18 .25 .29 .33 .24 .35 .41 .45 1 .17 .24 .30 U .20 .29 .34 .38 α = 1.75 α = 2 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .18 .58 .71 .78 .13 .42 .51 .56

.50 .46 .67 .77 .84 .63 .88 .99 U

.75 .32 .47 .56 .61 .42 .61 .71 .77 1 .26 .38 .45 .49 .32 .48 .56 .61

Table 4 (cont): Threshold value of x in flexible IT with Debt Targeting.

τ = .50 and ω = .50 α = 1.25 α = 1.5 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .52 .90 U U .66 U U U

.50 .27 .49 .61 .69 .58 U U U

.75 .19 .34 .42 .47 .38 .68 .85 .96 1 .15 .27 .33 .37 .29 .52 .64 .72 τ = .75 and ω = .50 α = 1.25 α = 1.5 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .33 .55 .66 .72 .78 U U U

.50 .17 .29 .35 .39 .35 .58 .70 .77

.75 .12 .20 .24 .27 .23 .39 .47 .52 1 .10 .16 .19 .21 .18 .29 .36 .40 τ = 1 and ω = .50 α = 1.25 α = 1.5 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .24 .38 .45 .49 .53 .77 .87 .93

.50 .12 .20 .24 .26 .25 .39 .46 .51

.75 .09 .14 .16 .18 .16 .26 .31 .35 1 .07 .11 .13 .14 .12 .20 .24 .26 τ = .50, ω = .50, and ψ = .20 α = 1.25 α = 1.5 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .43 .79 .97 U .75 U U U

.50 .22 .43 .54 .61 .48 .89 U U

.75 .16 .29 .37 .42 .32 .60 .75 .86 1 .12 .23 .28 .32 .24 .45 .57 .64 α = 1.75 α = 22

χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10 .25 .19 .61 .75 .82 .25 .44 .55 .60 .50 .82 U U U .75 U U U .75 .50 .93 U U .73 U U U 1 .37 .69 .87 .99 .51 .95 U U

1 Rz = .30 and Ω = 5. All other parameters take their base case values in Table 2. U indicates that the equilibrium is unique. 2 In the runs for χ = .25 - .75, the equilibrium is indeterminate at low values of x. The lower bound ranges from .01 to .15.

Table 5: Threshold value of Rz/x when the fiscal rule targets the ratio of debt to current output.

Threshold value of Rz for strict forward-looking IT when γ = .05 Scenario x = .3 x = .4 x = .5 x = .6 x = .7 x = .8

μ = 0 10.0 6.2 3.9 2.4 1.3 .44 μ = .25 8.1 4.2 1.9 .3 Unstable for x > .622 μ = .50 6.1 2.2 Unstable for x > .490 μ = .75 4.1 .2 Unstable for x > .404 μ = 1 2.1 Unstable for x > .345

Threshold value of x for flexible IT when τ = .50

Scenario α = 1.25 α = 1.5 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .31 .55 .28 .19 .28 .21 .15 .11

.50 .28 U U U .34 .55 .28 .19

.75 .33 U U U .31 U .72 .38 1 U U U U .30 U U U α = 1.75 α = 2 χ γ = .025 γ = .05 γ = .075 γ = .10 γ = .025 γ = .05 γ = .075 γ = .10

.25 .15 .17 .13 .10 .12 .15 .12 .09

.50 .42 .27 .18 .13 .28 .21 .15 .11

.75 .35 .55 .28 .19 .40 .32 .20 .14 1 .32 U .50 .29 .35 .55 .28 .19

-E1, E2+E3

-E1

E2+E3

R Z

-E1, E2+E3

E2+E3

-E1

x

R Z*

x *0

0

Unique

Indet

Unstable

Indet

0.0 0.2 0.4 0.6 0.8

x

2

4

6

8

10

W

Figure 2: Borderline value of W compatible with a unique equilibrium

when Rz = .20 and the real wage is perfectly flexible.

E4+E5, -(E1+E2+E3)E4+E5 (x = 0)

E4+E5 (x = x) 1

-E1

E2+E3

xx *x1W W W1 0

Figure 3: The relationship between infrastructure’s share of fiscal adjustment and the threshold value of the q-elasticity of private investment compatible with a unique equilibrium.

Unique

Indet

Unstable

Indet

Flex-wage solution

0.0 0.2 0.4 0.6 0.8

x

10

20

30

40

W

Figure 4: Borderline value of W compatible with a unique equilibrium

when Rz = .20 and the real wage is temporarily rigid (h = 1).

2 IT, LICs, Infra, Graphs, December 2014.nb

Unique

Indet

Unstable

Indet

Χ = 0 Uniquenss Region

0.0 0.1 0.2 0.3 0.4 0.5 0.6

x

10

20

30

40

50

60

W

Figure 5: Borderline value of W compatible with a unique equilibrium in the flex-wage model

when Rz = .20 and the coefficient on real output in the Taylor rule is .15.

Out[57]=

Unique

Indet

Unstable

Indet

Χ = 0 Uniquenss Region

0.0 0.1 0.2 0.3 0.4 0.5 0.6

x

10

20

30

40

50

60

W

Figure 6: Borderline value of W compatible with a unique equilibrium in the flex-wage model

when Rz = .30 and the coefficient on real output in the Taylor rule is .15.

IT, LICs, Infra, Graphs, December 2014.nb 3

Unique

Unstable

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Χ

5

10

15

20

25

W

Figure 7: Borderline value of Rz compatible with a unique equilibrium in the flex-wage model when

x = .50, W = 1, and the interest rate is set by a modified forward-looking Taylor rule.

4 IT, LICs, Infra, Graphs, December 2014.nb

Unique Unstable

Uniqueness Region for the

Pure Forward-Looking Rule

0.2 0.4 0.6 0.8

10

20

30

40

W

Figure 8: Borderline value of W compatible with a unique equilibrium in the flex-wage model

when Rz = .20 and the interest rate is set by a pure contemporaneous Taylor rule.

IT, LICs, Infra, Graphs, December 2014.nb 5

Out[13]=

Unique

Indet

Unstable

Indet

0.0 0.1 0.2 0.3 0.4 0.5

x

2

4

6

8

W

Figure 9: Borderline value of W compatible with a unique equilibrium

under a debt-targeting rule when Γ = .05 and Rz = .20.

6 IT, LICs, Infra, Graphs, December 2014.nb

Out[46]=

Γ = .025

Γ = .05

Γ = .10

Γ = .075

BBR

0.0 0.1 0.2 0.3 0.4 0.5 0.6

x

2

4

6

8

10

12

W

Figure 10: Comparing the determinacy region under a balanced budget rule with the determinacy

region for alternative values of Γ under a debt targeting rule when Rz = .20.

IT, LICs, Infra, Graphs, December 2014.nb 7