the real effects of inflation in a developing economy with external debt and sovereign risk

Please cite this article in press as: Assibey-Yeboah, M., & Mohsin, M. The real effects of inflation ina developing economy with external debt and sovereign risk. North American Journal of Economicsand Finance (2014), http://dx.doi.org/10.1016/j.najef.2014.07.004

ARTICLE IN PRESSG ModelECOFIN 460 1–16

North American Journal of Economics and Finance xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

North American Journal ofEconomics and Finance

The real effects of inflation in a developingeconomy with external debt and sovereign risk

Mark Assibey-Yeboaha, Mohammed Mohsinb,∗Q1

a Parliament of Ghana, Parliament House, Accra, Ghanab Department of Economics, The University of Tennessee, Knoxville, TN 37996, USA

a r t i c l e i n f o

Article history:Received 25 October 2012Received in revised form 24 July 2014Accepted 28 July 2014

JEL classification:E52F32F41O40

Keywords:Monetary policyCash-in-advanceExternal debtRisk premium

a b s t r a c t

In this paper we develop an intertemporal optimizing model toexamine the real effects of inflation induced by monetary policyin an open developing economy with external debt and sovereignrisk. The economy faces an upward sloping supply curve of debt.In our model, households require real balances in advance for con-sumption expenditures, and monetary policy involves targeting theinflation rate. We show that an increase in the inflation rate leadsto a decrease in the stock of foreign debt. It also leads to a decreasein consumption, employment, capital accumulation and output inthe long run. Our results show that the accumulation of foreigndebt exhibits non-monotonic adjustment. Particularly, an increasein the inflation rate leads to a current account surplus followed by adeficit. Along with this non-monotonicity, our model also explainsthe positive correlation between savings and investment during thetransitional periods (Feldstein–Horioka puzzle).

© 2014 Published by Elsevier Inc.

1. Introduction

Inflation is a major economic issue that takes prominence in policy discussions in many countries.It is more pronounced in developing countries, where governments frequently finance deficits bycreating money. As a result, over the past few decades, many central banks have set inflation targets

∗ Corresponding author. Tel.: +1 865 974 1690; fax: +1 865 974 4601.E-mail address: [email protected] (M. Mohsin).

http://dx.doi.org/10.1016/j.najef.2014.07.0041062-9408/© 2014 Published by Elsevier Inc.

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2 M. Assibey-Yeboah, M. Mohsin / North American Journal of Economics and Finance xxx (2014) xxx–xxx

as a means of keeping the rate of money growth in check. On top of the monetization, developingeconomies rely heavily on external borrowing to carry out their development programs. This leadsto the accumulation of substantial external debts with its attendant cost of debt servicing. With amajority of the world’s population living in developing countries, it is important to understand andgauge the prospects of economic development by examining the effects of monetary policy in theface of the increasing reliance on external capital. In this paper we develop a neoclassical monetarygrowth model to examine the effects of inflation induced by domestic monetary policy in a small opendeveloping economy with external debt and sovereign risk. A brief overview of the existing literaturewill adequately justify the need for this study.

The neoclassical monetary growth models,1 on which we put a lot of emphasis, are known to pro-duce conflicting results.2 First, Tobin (1965) argued that higher inflation is associated with highercapital stock and output.3 Using an optimizing model with money-in-the utility (MIU), Sidrauski(1967) rejected Tobin’s result by showing that monetary policy is superneutral in the long run. Onthe other hand, Stockman (1981), Abel (1985), Lucas and Stokey (1987), Dotsey and Sarte (2000) andothers consider cash-in-advance (CIA) economies to show that inflation has a negative effect on out-put in the long-run.4 The open economy literature has always shown ample interest in the effects ofmonetary policy on output, employment and the current account. The seminal papers which considerpolicy issues in an optimizing framework are by Obstfeld (1981a, 1981b). In both papers, he uses theMIU framework and employ Uzawa type preferences and claims that though in the short-run higherinflation leads to lower level of consumption and demand for real balances, the economy in the long-run will experience current account surplus and higher level of consumption. It is important to notethat Obstfeld (1981b) considers the policy effects for such an economy when the central bank fixesthe rate of growth of money whereas Obstfeld (1981a) assumes that the central bank fixes the rateof devaluation of the domestic currency. Though the findings are very similar, the analysis is con-siderably simplified if one assumes that the central bank targets the rate of change of the exchangerate (or domestic inflation rate). It is also well known that the steady state policy effects are the sameregardless of whether the central bank fixes the rate of growth of money or the inflation rate.5

In spite of the huge contributions to the open economy monetary growth literature, Obstfeld’s stud-ies are limited on many grounds. First, as the model deals with an endowment economy, it precludesany discussion of the effects of monetary policy on employment, output, and investment. Second, theMIU framework that he employed is used in a relatively narrow set of subfields in macroeconomics.The CIA approach to introducing money into a model, rather, is more widely used, especially in theempirical asset pricing literature. Third, he employed Uzawa preferences to overcome the problem

1 These models assume perfect flexibility of prices and wages. Markets always clears as there are no institutional rigidities.Generally, the monetary authority is assumed to control the growth rate of money supply. Alternatively, one could implementinflation targeting, but not both in the same model.

2 There is another class of models, though, with price and wage rigidities. These new-Keynesian models rely on nominal pricerigidities to generate frictions to provide non-neutral effects of monetary policies. The labor market does not necessarily clear atall times, hence, policymakers deal with actual and potential (full-employment) levels of output and employment. Policymakersalso deal with actual inflation and inflation gaps. The monetary authority often follows Taylor-type rules to conduct monetarypolicies. For details, see Clarida, Gali, and Gertler (1999), Obstfeld and Rogoff (1995), Ida (2011) and Woodford (2003). Becauseof these fundamental modeling differences, the results of these new-Keynesian models are often different from the neoclassicalmonetary growth models at various levels.

3 Romer (1986) finds empirical support for the Tobin effect. In another empirical study, Grier and Grier (2006) find that infla-tion uncertainty lowers output growth, while the direct effect of average inflation on output is actually positive and significantfor Mexico.

4 Barro (1996) provides empirical evidence that inflation has a negative effect on economic growth. Kalirajan and Singh(2003) also empirically conclude that any increase in inflation from the previous period negatively affects growth in India.For Thailand, Indonesia, Mexico, and Chile, Assibey-Yeboah and Mohsin (2012) find that inflation is negatively correlated withconsumption, investment and the stock of foreign debt.

5 Hence, the assumption that the central bank targets the rate of change of the exchange rate implies that the central bankmay possibly be intervening in the foreign exchange market to some extent only during the adjustment period before the steadystate. Also, as we will see, instead of intervening in the foreign exchange market the central bank could adjust the rate of growthof money appropriately.

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of degenerate dynamics.6 These issues are adequately addressed in Mansoorian and Mohsin (2006).They instead assumed a fixed rate of time preference. However, like Obstfeld (1981a), they simplifiedtheir analysis by assuming that the central bank targets the domestic inflation rate and not the rateof growth of money. Along with labor/leisure choice and CIA constraint(s),7 the study shows that anunanticipated permanent increase in the domestic inflation rate will lead to a fall in consumption,investment and employment. Nevertheless, the current account goes into a surplus as the fall in con-sumption and investment dominate the fall in output. They also report that temporary changes indomestic inflation rates have permanent effects in the economy.

These open economy monetary models too provide no clear-cut conclusions. Moreover, these stud-ies assume perfect capital mobility, by which the supply of debt to the economy is perfectly elastic.This assumption is questionable for developing economies with an external borrowing constraint andsovereign risk. The risk that a borrower will default on a loan affects the market interest rate. The costof borrowing is often an increasing function of the stock of debt. This observation was originally doc-umented by Bardhan (1967) and later incorporated in Bhandari, Haque, and Turnovsky (1990), Fisher(1995), Tuladhar (2003), Schmitt-Grohe and Uribe (2003), and Chatterjee and Turnovsky (2007) toaddress different open economy macroeconomic issues. In this paper we will also incorporate thisidea to investigate the effects of monetary policy in a developing economy.

Before we outline our model, we need to draw special attention to two other papers that alsostudy the effects of monetary policies in small open economies with imperfect capital markets. First,Tuladhar (2003) examines the implications of alternative monetary policy rules and the choice ofinstruments and targets in a small open economy within a new-Keynesian framework and Calvo-style nominal price rigidities. Specifically, Tuladhar compares a benchmark efficient markets modelwith a monetary targeting regime and three different inflation targeting rules (namely, Taylor type, CPIinflation, non-tradable inflation). As noted earlier, these modeling features differ fundamentally fromthat of our proposed model. In fact, our proposed model has more similarities with Assibey-Yeboahand Mohsin (2012). They proposed a simple model to support their empirical findings that inflationis negatively correlated with consumption, investment and the stock of foreign debt. They show aneconomy with inelastic labor supply and imperfect capital mobility supports those empirical findingsif both households and firms hold real balances in advance for their expenditure.8 However, thismodel is limited as there is no labor/leisure choice for consumers, and it does not reflect employmenteffects of monetary policies. In addition, their model does not support the non-monotonic transitionaldynamics of the current account that is often reported in the empirical literature. The proposed modelwill address these concerns.

In our model households can make labor–leisure decisions. Firms produce output with labor andcapital as inputs. Similar to Obstfeld (1981a), Calvo (1987), Mansoorian and Mohsin (2006) and manyothers, we assume that monetary policy is conducted by controlling inflation. Moreover, we adopt theCIA framework as it is more appropriate in developing economies, where the credit market is not welldeveloped. We show that a permanent increase in the inflation rate will lead to a fall in consumption,since with CIA constraint on consumption, the higher inflation rate increases the price of consumptionrelative to leisure, inducing the representative household to substitute leisure for consumption. Theresulting fall in labor input in the production process reduces the marginal productivity of capital,leading to a fall in investment. Higher inflation also leads to a lower level of foreign debt in the longrun due to the decreased level of output in the economy.9

6 For a well-defined steady state to exist (in a small open economy model without ongoing growth), one should assume thatthe rate of time preference is equal to the world rate of interest. This restriction, in fact, poses a serious limitation for studyingthe dynamic effects of government policies. To overcome this, Obstfeld used Uzawa type preferences. Here, the rate of timepreference is an increasing function of instantaneous utility which was required for saddle point stability rather than for anyeconomic reason.

7 Other related papers which employ CIA constraints in an open economy setting include Calvo (1987), Calvo and Vegh (1995)and Edwards and Vegh (1997).

8 In their model, the negative effect on investment is directly due to investment being subject to CIA constraint as higherinflation acts as a tax on investment. Without this restriction there will be no real steady state effects in the economy.

9 In our model labor/leisure choice plays a pivotal role in terms of steady state and transition effects. To demonstrate this,we re-evaluate our model under inelastic labor supply and the results are drastically different.

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The adjustments of all the major variables are non-monotonic in nature. Our calibration exer-cise reveals that even though capital decreases throughout the transitional period, the initial rate ofdecline of investment is higher than it is during the later part of the adjustment period. The initial fallin employment actually decreases the marginal productivity of capital. After the initial jump, employ-ment continues falling for a while before it starts increasing to reach the new steady state. On theother hand, after its initial fall, consumption grows during the early transitional period before it startsdeclining again to reach its steady state level. We observe non-monotonic adjustment of the accumu-lation of foreign debt; initial decrease followed by gradual increase. Since the negative of foreign debtmeasures the current account position of the economy, we can claim that the current account balanceof the economy exhibits a non-monotonic adjustment due to a permanent inflationary shock in theeconomy. During the initial transitional period the current account position improves, then deterio-rates gradually. Interestingly, during the major part of the transitional period we observe a positivecorrelation between savings and investment (Feldstein–Horioka (1980) puzzle). Interestingly, pre-vious open economy monetary growth models within the neoclassical setup could not support thisstylized fact.

The rest of the paper is organized as follows. The main model and its findings is presented inSection 2. Section 3 outlines the model with labor–leisure choice, and the concluding remarks aregiven in Section 4.

2. The model

The model is that of a small open economy that produces a single traded and non-storable good.It comprises three key sectors: households, firms, and the government. Domestic firms are owned byhouseholds, to whom profits accrue. The small economy cannot influence the foreign currency price.The domestic price of the good, Pt is linked to the foreign price by:

Pt = EtP∗t , (1a)

where Et is the nominal exchange rate (the price of foreign currency in terms of domestic currency).Taking a time derivative of Eq. (1a) yields

�t = εt + �∗t , (1b)

where �t (≡ Pt/Pt) is the domestic inflation rate, εt (≡ Et/Et) is the rate of change of the exchange rate,and �∗

t (≡ P∗t /P∗

t ) is the foreign inflation rate. We assume that the foreign price of the good is fixed atP∗. With flexible prices, the change in the rate of inflation is equal to the rate of depreciation of thedomestic currency (�t = εt).

Unlike the standard assumption of perfect capital mobility where a small open economy can borrowat a fixed world interest rate, r∗, we assume that a developing economy is required to pay an addi-tional risk premium. The country-specific risk premium, Z, depends on debt-servicing ability. Thus,the effective interest rate for the economy, rt , is given as

rt = r∗ + Z(

bt

f (kt, lt)

); Z′ > 0, (2)

where, bt denotes the stock of foreign debt, f(kt, lt) shows the output level of the economy, kt showsthe stock of capital, and lt denotes labor supply. The possibility of a cutoff in debt is captured by theassumption that the function Z(.) is convex (Z′′>0).10 We proceed by considering the problem facingQ2each sector in turns.

10 The country-specific risk premium, Z, is modeled differently in different studies. For example, Fisher (1995) and Schmitt-Grohe and Uribe (2003) assumed it to depend on the level of debt, Haque and Turnovsky (1990), and Chatterjee and Turnovsky(2007) assumed it to depend on the debt-capital ratio. In Tuladhar (2003), the risk premium depends on the change in thenet foreign assets or the foreign capital flow. In our case, it depends on the economy’s creditworthiness captured by debt-output ratio. Though we are not the first to introduce such debt-elastic interest rate, but to the best of our knowledge, weare incorporating this to offer a comprehensive monetary growth model of a developing economy within the neoclassicalframework.

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2.1. The representative household

The representative household with an infinite planning horizon, faces imperfect capital markets,and has perfect foresight. The agent chooses his private rate of consumption, ct and labor supply, lt, inorder to maximize the present value of lifetime utility, U, as given by:

U =∫ ∞

0

u(ct,lt)e−ˇtdt, (3)

where ˇ(> 0) is the fixed rate of time preference. For simplicity we assume that the utility function isadditively separable in ct and lt; i.e. u(ct, lt) = U(ct) + V(lt), with U′(ct) > 0, U′′(ct) < 0, V′(lt) < 0 and V′′(lt) < 0.Thus, the representative agent is assumed to derive positive, but diminishing, marginal utility fromconsumption and leisure. In addition we assume that u(.) also satisfies lim

ct→0u′(.) = ∞.

The representative household also receives monetary transfer with real value �t from the govern-ment. Money is introduced through a cash-in-advance constraint, with the household requiring realmoney balances mt to finance his consumption expenditures:

mt≥ct. (4)

The net real assets, at held by the representative household:

at = mt − bt. (5)

His flow budget constraint is given by:

at = Dt + wtlt + �t − rtbt − ct − �tmt, (6)

where Dt is the total dividend received by the representative household, wt is the real wage rate and�tmt is the “inflation tax” on real balances. Eq. (6) implies that the agent will accumulate assets to theextent that his total wealth exceeds his total expenditure.11

The household’s problem, therefore, is to maximize (3), subject to (4)–(6), and the initial condition,

a(0) = a0. The agent must also satisfy the No-Ponzi game condition limt→∞

ate

∫ t

orsds � 0. As the return

from debt repayment dominates the return from real balances, Eq. (4) will hold with strict equality.Setting mt = ct, the current-value Hamiltonian for the household’s problem may be written as:

H = U(ct) + V(lt) + �t[Dt + wtlt + �t + rtat − (1 + rt + �t)ct]. (7)

where �t, the co-state variable associated with (6), is the marginal utility of wealth (or marginal utilityof reducing debt for a borrower). In making his decisions, the household takes rt and �t as given. Weobtain the following first-order optimality conditions:

U ′ (ct) = �t

(1 + r∗ + Z

(bt

f (kt, lt)

)+ �t

), (8a)

V ′ (lt) = −�twt, (8b)

�t = �t

( − rt

), (8c)

and the standard transversality condition limt→∞

�tat = 0. Eq. (8a) equates the household’s marginal cost

and benefit of postponing one unit of current consumption. (8b) equates the marginal disutility oflabor to the real wage valued at the shadow value of wealth, while (8c) shows how the marginalutility of wealth evolves.

11 To see how (6) is derived note that mt = MtPt

and bt = Bt PBtPt

= BtPt

, where Pt is price level, PBt is nominal unit price of foreigndebt and Bt the quantity of foreign debt. For simplicity we set PBt = 1 so that one unit of output could be equivalent to one unit of

real debt (in terms of repayment). Hence mt = MtPt

− �tmt and bt = BtPt

− �tbt , where the rate of inflation �t = PtPt

. Incorporating

these results into the representative agent’s nominal budget constraint Ptct + Mt − Bt = Pt(Dt + wtlt ) − itBt + Pt�t one obtainsEq. (6). Here, it is nominal interest rate. Note that the nominal values of the relevant variables are in local (domestic) currency.However, we convert all the variables in real terms for our analysis.

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2.2. The representative firm

The representative firm produces output with a neoclassical constant returns to scale productionfunction exhibiting positive, but diminishing, marginal physical productivity in capital and labor; i.e.yt = f(kt, lt): fk > 0, fl > 0, fkk < 0, fll < 0 and fkkfll − f 2

kl= 0. Investment involves adjustment costs given by

the function:

˚(It) = It + � (It), (9)

where ˚(It) is the total cost associated with the purchase of It units of new capital, and � (It) arethe adjustment costs associated with It. The function � (It) is assumed to be a nonnegative, convexfunction, with ˚′ ≥ 0; ˚′′ > 0. In addition, we may set � (0) = 0 and � ′(0) = 0, which means that the costof zero investment is zero, ˚(0) = 0 and the marginal cost of initial investment is unity, ˚′(0) = 1. Thedividend payment net of investment expenditure is

Dt = f (kt, lt) − wtlt − ˚(It). (10)

The firm’s problem is to maximize the present value of its dividend payments:∫ ∞

0

Dte−∫ t

0rvdv

dt =∫ ∞

0

[f (kt, lt) − wtlt − ˚(It)]e−∫ t

0rvdv

dt, (11)

subject to:

kt = It, (12)

and the initial condition k(0) = k0. For simplicity we assume that there is no depreciation of capital.The current value Hamiltonian for the firm’s problem is:

H = f (kt, lt) − wtlt − ˚(It) + qtIt, (13)

where qt, the co-state variable associated with the state variable kt, is the shadow price of capital. Thefirst-order optimality conditions for this problem with respect to lt, It, and kt are, respectively:

fl(kt, lt) = wt, (14a)

˚′(It) = qt, (14b)

qt = qt rt − fk(kt, lt), (14c)

and the transversality condition limt→∞

qtkt = 0.

2.3. The government (or monetary authority)

The government in this model is kept very simple on purpose. We abstract completely from fiscalpolicies and focus solely on monetary policy. Thus the “government” represents the monetary side ofthe economy. Due to our simplicity, the entire revenue of the government is in the form of seigniorageand it must be transfered back to the households to restore general equilibrium. The nominal budgetconstraint of the government is given by Mt = Pt�t . For a given price level, the change in the nominalmoney supply is solely determined by �t. In other words, the change in real money supply (Mt/Pt) isequal to real monetary transfers to households, �t. Though the government adjusts the nominal moneysupply to conduct monetary policy, it is following a guiding rule to achieve the desired outcome. Itturns out that the monetary authority could choose the real monetary transfers �t in order to achieve adesired inflation rate �t. This will be very clear once we convert the nominal equation into real terms.As shown in footnote 11, the nominal budget constraint (Mt = Pt�t) could be re-written in real termsas follows:

mt + �tmt = �t. (15)

Eq. (15) implies that government expenditure, which consists of real monetary transfers �t shouldbe equal to total government revenues from seigniorage (mt + �tmt). As outlined earlier, we assume

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that the central bank targets the inflation rate (�t), by continuously adjusting the transfers �t. This isvery common in the literature. See Obstfeld (1981a), Calvo (1987) and Mansoorian and Mohsin (2006)for details. What do we gain by this simplification? In the traditional framework the authority simplycontrols the growth rate of money supply and as a result the inflation rate becomes endogenous andvariable off the steady state. This then increases the dimension of the dynamic system. By assuminginflation targeting, as set up, we are in fact simplifying a lot. As we will see in the following section,the dynamic structure of the model is a fourth order system, without which compromise, the systemwould have been of fifth order. We must note that the cost of this approximation is very negligible.Though there is some approximation error during the transitional periods, in terms of steady stateeffects, there is no approximation error. It well known (and can be shown easily) that the steady statepolicy effects are the same, regardless of whether the central bank fixes the rate of growth of moneyor the inflation rate.

2.4. Equilibrium dynamics

By combining all the optimality conditions derived from the household and firm sectors, togetherwith the flow budget constraints, equilibrium dynamics of the economy can be described by thefollowing set of equations:

U ′(ct) = �t

[1 + r∗ + Z

(bt

f (kt, lt)

)+ �t

], (16a)

V ′ (lt) = −�tfl(kt, lt), (16b)

�t = �t

[ − r∗ − Z

(bt

f (kt, lt)

)], (16c)

˚′(It) = qt, (16d)

qt = qt

[r∗ + Z

(bt

f (kt, lt)

)]− fk(kt, lt), (16e)

kt = It, (16f)

bt =[

r∗ + Z(

bt

f (kt, lt)

)]bt + ct + ˚(It) − f (kt, lt). (16g)

It should also be noted from (16a), (16b), and (16d) that the equilibrium levels of ct, lt and It can berepresented by the following equations:

ct = c(�t, kt, �t, bt), (17a)

lt = l(�t, kt), (17b)

It = I(qt). (17c)

We are now in a position to analyze the dynamics of the model. The dynamic behavior of theeconomy is determined by the following system of differential equations, (18a)–(18d). Noting thatct = c(�t, kt, �t, bt), lt = l(�t, kt), and It = I(qt), we obtain

bt =[

r∗ + Z(

bt

f (kt, l(�t, kt))

)]bt + c(�t, kt, �t, bt) + ˚(I(qt)) − f (k, l(�t, kt)), (18a)

�t = �t

[ − r∗ − Z

(bt

f (kt, l(�t, kt))

)], (18b)

kt = I(qt), (18c)

qt = qt

[r∗ + Z

(bt

f (kt, l(�t, kt))

)]− fk(kt, l(�t, kt)). (18d)

The dynamic structure of the system (18) is a fourth order system with two predetermined variables(b and k) and two jump variables (� and q). For saddle point stability the coefficient matrix must have

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two negative and two positive eigenvalues. The details of the linearized system is outlined in theAppendix.

It is important to highlight the role of investment adjustment costs in this model. In general, in amodel with adjustment costs, capital adjusts slowly and does not make a discrete jump (like a con-trol variable) at the time of policy changes. It also reduces the volatility of investment. However, inour model, adjustment costs play a bigger role. For better exposition, let us assume that we do nothave any adjustment costs function. Following, from the firm’s problem, we will have qt = 1 in Eq.(14b) and rt = fk(kt, lt) in Eq. (14c). Recall that these are not steady state conditions, but rather musthold true at all times. The transitional dynamics between k and q will thus collapse as investmentwill not be a function of q (see Eq. (16d) or (18c)). In such a setup, capital will discretely adjust tosteady state and display no transitional dynamics. The system will have only one negative eigen-value and there will be the absence of non-monotonic adjustment of the current account and othervariables.

2.5. The effects of inflation

In this section we analyze the long run effects of an unanticipated, permanent increase in inflation.Now we look at the steady state effects of an unanticipated and permanent increase in the inflationrate. At the steady state we must have � = q = k = b = 0. Thus, any variable xt is represented by x insteady state. The steady state is captured by the following equations:

U ′(c) = �t

(1 + r∗ + Z

(b

f (k, l)

)+ �

), (19a)

V ′ (l)

= −�fl(k, l), (19b)

ˇ = r∗ + Z

(b

f (k, l)

)(19c)

qt = 1, (19d)

fk(k, l) = r∗ + Z

(b

f (k, l)

), (19e)

f (k, l) =[

r∗ + Z

(b

f (k, l)

)]b + c. (19f)

These equations jointly determine the steady state equilibrium values of consumption c,labor supply l, capital stock k, debt accumulation b, marginal utility of wealth �, and theshadow price of capital q. The steady state effects of an increase in inflation, obtainedby differentiating the long-run equilibrium, i.e. Eqs. (19a)–(19f) with respect to � are asfollows:

dc

d�= �fl{(fkfkl − flfkk)(f − rb)}

�< 0, (20)

dq

d�= 0, (21)

dk

d�= �fklflf

�< 0, (22)

dl

d�= −�fkkflf

�< 0, (23)

db

d�= −b�(−flkfkfl + f 2

lfkk)

�< 0, (24)

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d�

d�= �fkkfV

′′

�< 0, (25)

where � = U′′(f − rb)(flkfkfl − fkkf 2

l) − (1 + r + �)fkkfV

′′< 0.

The steady state effects show that an increase in the inflation rate reduces the long-run marginalutility of wealth, debt, labor supply, and consumption. The intuition behind these results are given asfollows. In a CIA economy, the agent needs to hold real money balance in advance for consumption.Thus, depreciation of the domestic currency makes consumption relatively more expensive (in termsof leisure). As a result, consumption falls. To maximize his utility, the agent consumes more leisure,leading to a decrease in labor supply. With the labor supply decreasing, the marginal productivityof capital will decline. This will lead to a decline in investment. From y = f (k, l), we can easily verify(using (22) and (23)) that

dy

d�= fk

dk

d�+ fl

dl

d�< 0. (26)

As such the production level of the economy will fall. Also, in equilibrium, the marginal productivityof capital is fixed. Hence, both capital and labor will decline proportionately. It should also be notedthat in the steady state the effective real interest rate in the small developing economy is fixed andequal to the rate of time preference. This implies that the risk premium paid by the economy in thenew equilibrium is the same as it was initially. This is only possible if the debt position and the outputlevel also change proportionately.12 This explains why the net foreign debt declines in the steady state.

2.6. A numerical evaluation

In this section we perform a detailed numerical evaluation of our model. This is important for manyreasons. First, because of the complex nature of the model, we are unable to show analytically thatthe model has saddle point stability. With reasonable functional forms and parameter values, we cannumerically show that the coefficient matrix in (A.8) has two negative and two positive roots. Second,since the models involve fourth order differential equation systems with two stable roots, we cannotobtain simple phase diagrams as well as the optimal paths (transitional dynamics) of all the majorvariables easily. A numerical evaluation will help us immensely in this regard. Third, we can easilyperform sensitivity analysis for different parameter values to evaluate the effectiveness of monetarypolicy. Finally, it should also be noted that the real purpose of this calibration exercise is not intendedto match the real world data, rather that it aims at providing further insights into the qualitativebehavior of economic variables subject to reasonable bounds.

To begin, we specify functional forms for the production function, utility function and the upwardsloping supply curve of debt. Following the Real Business Cycle (RBC) literature, we assume that the

instantaneous utility exhibits constant relative risk aversion, U(c, 1 − l) = (c1−˛(1−l)˛)1−�−1

1−� , and theproduction function is Cobb Douglas, y = k l1− . The functional form of the upward sloping supply

curve of debt is specified as r = r∗ + ea b

f (k,l) − 1 (see Chatterjee & Turnovsky, 2007). Following Cooleyand Prescott (1995) and Chatterjee and Turnovsky (2007), we set the share parameter for leisure,

= 0.36, and capital’s share in output, = 0.32. In addition, we set the premium on borrowing, a = 0.25,the world interest rate r∗ = 0.06, the rate of time preference, = 0.10, and the initial inflation rate,� = 0.10. The relative risk aversion parameter is set to � = 2.1. To obtain the initial steady state, wesubstitute these parameter values into the steady state Eqs. (19a)–(19f). The steady state level of

12 It is important to note, however, that our model economy is a typical neo-classical (Ramsey type) growth economy, wherethe variables in per capita terms do not grow in the steady state. This means that in the long run our model must satisfy� = q = k = b = 0. So, the country will not get rid of foreign debt in the steady state. In fact, as the economy reaches its steadystate, the economy will neither experience accumulation nor deccumulation of foreign debt. It will be clearer, further, once

we recall Eq. (19c). In the steady state, Z

(b

f (k,l)

)= − r∗ . From our modeling feature, it is also clear that both and r∗ are

constants. Thus, both foreign debt and output must change proportionately and in the same direction as well.

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t

L

L1

L0L2

0

Fig. 1. Time path of the level of employment.

t

b

b1

b2

0

Fig. 2. Time path of the stock of debt.

consumption is 0.86, labor supply is 0.51, capital stock is 2.80, stock of debt is 0.14 and output is 0.87.Now we calculate the steady state effects of an increase in the inflation rate from 10% to 15%. Capitalstock and employment both decrease by 2.02 percent. As a result of this inflationary shock, outputalso decreases by 2.02 percent. At the same time we observe a 2.02 percent decline in the stock offoreign debt. It should be recalled that at the steady state the rate of time preference (which is fixed byassumption) should be equal to the effective interest rate faced by the economy. This means that therisk premium in both equilibria must be the same (4% in this example), which can only be obtained ifboth debt and output change proportionately.

As part of our numerical exercise, we calculate the short run effects too. At t = 0 when the inflationaryshock is implemented, there are no short run effects on the stock of debt and the level of capital as bothof them are predetermined variables. Consumption initially declines from 0.86 to 0.85, a 1.10 percentdecrease. On the other hand, employment decreases from 0.51 to 0.49, a 2.57 percent decrease. Thus,both consumption and employment decline in the short run. The detailed adjustments of the levelof employment, the stock of debt, consumption, and the capital stock are given in Figs. 1, 2, 3, and 4,respectively.

We now outline the transitional response of the economy to an unanticipated permanent increasein inflation. The transitional dynamics following the increase in � are derived from the linearizedsystem and are given in the Appendix. In this economy, an increase in the inflation rate makes con-sumption more expensive (in terms of leisure). Households respond by reducing consumption of goodsand increasing the consumption of leisure. Labor supply in the short run goes down as a result. Thoughin the short run capital does not change, output level will decrease due to lower employment. Thelower level of employment decreases the marginal productivity of capital and hence investment startsdeclining. As a result the capital stock starts falling. After the initial fall, consumption continues to

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t

c

c1

c0

c2

0

Fig. 3. Time path of consumption.

t

k

k1

k2

0

Fig. 4. Time path of the level of capital.

increase during the early transitional periods before it starts declining again. The detailed adjustmentpath of consumption is outlined in Fig. 3.

The adjustments of other major variables are non-monotonic as well. Our numerical exercisereveals that after an immediate downward jump, employment keeps dropping for a while and thengradually increases to reach its new steady state level (see Fig. 1). On the other hand, capital stockdecreases throughout the transitional period. However, the initial rate of disinvestment is higher thanit is during the later part of the transitional period. Fig. 4 outlines the adjustment path of capital stock.

One of the important results is the effect on the accumulation of foreign debt. Higher inflation in theeconomy leads to a lower level of foreign debt in the long run in real terms. This means that during thetransitional period the economy repays some of its outstanding foreign debt. Moreover, this processis non-monotonic. Its detailed adjustment path is given in Fig. 2. Our numerical exercise reveals thatthe economy deccumulates foreign debt during the very early phase of the adjustment process. Aftera short while, the economy starts accumulating debt again. The economic intuition is very clear. Itshould be noted that debt and capital are predetermined variables. In the short run, due to an decreasein employment, the output level goes down. As a result, the economy worsens its creditworthinessinstantly. With a higher effective cost of borrowing, it is not surprising that the economy starts toborrow less. However, the effective interest rate will adjust gradually towards its long run level andhence the initial falling trend of the foreign debt will be followed by a gradual increase. Overall,the economy will end up with a lower level of foreign debt. See footnotes 11 and 12 for furtherclarity. Now, if we focus our analysis in terms of current account adjustment, it means the currentaccount position of the economy exhibits a non-monotonic adjustment as well. During the initialtransitional period, the current account position improves, then it subsequently decreases. So duringthe major part of the transitional period, our model explains the positive correlation between savingsand investment – Feldstein–Horioka (1980) puzzle. For more discussions on the Feldstein–Horioka

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puzzle or positive correlation between savings and investment in open economy see Ioria and Fachin(2014) and Mansoorian and Mohsin (2010).

Since Mansoorian and Mohsin (2006) explicitly deal with the effects of inflation in a small openeconomy and our modeling features have much in common, it will be relevant to look into the dynamicadjustment of the macroeconomic variables in their study and compare it with our findings. Such com-parison will also highlight the role of the country-specific risk premium that is playing in our model. Inboth models we find steady state decreases in investment, employment, output and consumption. Thisis not surprising, though, as in both models CIA constraints play a similar role. Though in both modelsthe steady state effects on the net asset position is the same, the underlying reasons are significantlydifferent. The decreased debt position in our model is attributed to the upward sloping supply curve ofdebt (or risk premium) we deploy whereas in Mansoorian and Mohsin the result is attributable to theimposed intertemporal solvency condition. In addition, due to this intertemporal solvency condition,a temporary shock has a permanent effect in their model, which is not the case in ours.

One should also note that, in their model, the production and consumption sides are separable andas a result the transitional dynamics are also significantly different. For example, if we were to assumea separable preference in their model (as in our case) the transitional dynamics involving consumptionwill be significantly different. In that case, consumption depends on both the marginal utility of wealthand inflation, and takes a discrete jump to reach a new steady state given any external inflationaryshocks. In other words, due to ‘zero-root’ problem, consumption does not exhibit any transitionaldynamics. More importantly, due to non-monotonic adjustment of the current account, our modelcould account for a positive correlation between savings and investment during the transitional period.This is a serious limitation in Mansoorian and Mohsin. By introducing the risk premium, we couldovercome this limitation.

3. The model without labor/leisure choice

Here we consider a special case of our complete model where labor supply is completely inelastic(l = l). Setting l = lk = 0 in the full model we obtain the following dynamic system that controls thisfixed employment economy:

bt =[

r∗ + Z

(bt

f (kt, l)

)]bt + c(�t, bt, kt, �t) + ˚(I(qt)) − f (kt, l), (27a)

t = t

[ − r∗ − Z

(bt

f (kt, l)

)], (27b)

kt = I(qt), (27c)

qt = qt

[r∗ + Z

(bt

f (kt, l)

)]− fk(kt, l). (27d)

We could easily linearize the above system as we did in (A.8) in the appendix to demonstrate thatthe model has saddle point stability. Once again, the system has two predetermined variables (b andk) and two jump variables ( and q). For saddle point stability the coefficient matrix of the linearizedsystem must have two negative and two positive eigenvalues. In this special case we can easily provethat the system is saddle point stable.

Now we examine the impact of an unanticipated and permanent increase in the inflation rate onsteady state levels of the variables. The steady state is captured by the following equations:

U ′ (c) = �

(1 + r∗ + Z

(b

f (k)

)+ �

), (28a)

= r∗ + Z

(b

f (k)

)(28b)

q = 1, (28c)

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fk(k) = r∗ + Z

(b

f (k)

), (28d)

f (k) =[

r∗ + Z

(b

f (k)

)]b + c. (28e)

These equations jointly determine the steady state values of the variables. It is clear from theabove equations that under this situation there is no real steady state effects. In steady state, marginalproduct of capital is fixed at ˇ. Since there is no labor involved in the production process, it meansthat there must be a unique level of capital stock in the steady state. This also means that output levelwill remain unchanged. Now, from Eq. (28b) it is also clear that in steady state debt/output ratio isalso unchanged. This implies that there will be no effect on stock of foreign debt as well. Finally, it isalso clear that consumption will remain unchanged in the steady state. Since capital and debt are twopredetermined variables and they are unchanged, there is no transitional dynamics under this specialcase. These results with inelastic labor supply are significantly different from our complete model. Inother words, labor/leisure choice plays a pivotal role in our complete model. In this context, it is alsowarranted that we compare our results with that of Assibey-Yeboah and Mohsin (2012) where theyalso assumed inelastic labor supply. Needless to say, these two models support significantly differentresults.

4. Concluding remarks

In this paper, we study the dynamic macroeconomic effects of monetary policy aimed at targetinginflation rate. We consider a small open economy with an external debt and sovereign risk – a typicaldeveloping economy. Our economy faces an upward sloping supply curve of debt as well. Householdshold money for consumption expenditure and can make labor/leisure choice to maximize welfare.Firms maximize profits, and investment is subject to adjustment costs. We show that an increasein inflation rate lowers the level of investment, employment, production and consumption in thelong run. However, the economy could lower its level of foreign debt. All the major variables exhibitnon-monotonic transitional dynamics. Interestingly, our model is capable of explaining the positivecorrelation between savings and investment – the well known Feldstein–Horioka (1980) puzzle.

There are various limitations that could be addressed in future research. The model is deterministicin nature. As a result, we are not able to evaluate the effects of monetary policy when the economyis subject to other shocks like productivity shocks and shocks involving foreign interest rates andterms of trade. To adequately address these concerns one needs to adopt a dynamic stochastic generalequilibrium (DSGE) framework. Unfortunately, that is beyond the scope of this paper.

Uncited references Q3

Mishkin (2000), Mohsin (2006), and Turnovsky (1997).

Acknowledgements

We sincerely thank three anonymous referees and the editor for their constructive comments andsuggestions. All remaining errors or omissions are the responsibility of the authors.

Appendix A. Equilibrium dynamics

Recall the equations from where the equilibrium levels of c, l and I are solved:

ct = c(�, k, �, b), (A.1)

lt = l(�, k), (A.2)

It = I(q), (A.3)

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with the corresponding partial derivatives: c� = f 2[1+r+�]−�Z ′bf l l�f 2U′′ (c)

, c� = �U′′ (c)

< 0, cb = �Z ′

fU′′

(c)< 0, ck =

− �Z ′bf k

U′′ f 2 > 0, l� = − flV ′′ (l)+�fll

> 0, lk = − �flkV ′′ (l)+�fll

> 0, and Iq = 1˚′′ > 0.

The dynamic behavior of the economy is determined by the following system of differential equa-tions:

b =[

r∗ + Z(

b

f (k, l(�, k))

)]b + c(�, b, k, �) + ˚(I(q)) − f (k, l(�, k)), (A.4)

� = �[

ˇ − r∗ − Z(

b

f (k, l(�, k))

)], (A.5)

k = I(q), (A.6)

q = q[

r∗ + Z(

b

f (k, l(�, k))

)]− fk(k, l(�, k)). (A.7)

The above dynamic structure of the model is a fourth order system, which may be expressed inlinearized form about the steady-state equilibrium as follows:

⎡⎢⎢⎣

b

�

k

q

⎤⎥⎥⎦ =

⎡⎢⎢⎢⎢⎣

a11 a12 a13 a14

a21 a22 a23 0

0 0 0 a34

a41 a42 a43 a44

⎤⎥⎥⎥⎥⎦

⎡⎢⎢⎣

b − b

� − �

k − k

q − q

⎤⎥⎥⎦ , (A.8)

where a11 =(

cb + r + bZ ′f

), a12 =

[c� −

(1 + b2Z ′

f 2

)fll�

], a13 =

[ck −

(1 + b2Z ′

f 2

)(fk + fllk)

],

a14 = Iq, a21 = − �Z ′f , a22 = �Z ′bf l l�

f 2 , a23 = �Z ′bf 2 (fk + fllk), a34 = Iq, a41 = qZ ′

f , a42 = −(

qZ ′bf l l�f 2 + fkll�

),

a43 = −[

qZ ′bf 2 (fk + fllk) + (fkk + fkllk)

], and a44 = ˇ.

All elements of the coefficient matrix in (A.8) are evaluated at their steady state values. The sys-tem has two predetermined variables (b and k) and two jump variables (� and q). For saddle pointstability the coefficient matrix must have two negative and two positive eigenvalues. Because of thecomplexity of the model, it is not possible to show saddlepoint stability analytically. Our numericalexercise, however, shows that the conditions for saddlepoint stability will be satisfied with reasonablefunctional forms and parameter values. Moreover, as a special case (in the model with inelastic laborsupply) we can easily show analytically that two of the eigenvalues are indeed negative.

Let the eigenvalues of the coefficient matrix in (A.8) be denoted by �1, �2, �3, and �4. Suppose �1and �2 are negative, while �3 and �4 are positive. Also, suppose (�i1, �i2, �i3, �i4) is the eigenvectorassociated with �i, ∀ i = 1, 2, 3, 4. Then we can write⎡

⎢⎢⎢⎢⎣

bt − b

t −

kt − k

qt − q

⎤⎥⎥⎥⎥⎦ =

⎡⎢⎢⎢⎢⎣

�11 �21 �31 �41

�12 �22 �32 �42

�13 �23 �33 �43

�14 �24 �34 �44

⎤⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎣

A1e�1t

A2e�2t

A3e�3t

A4e�4t

⎤⎥⎥⎥⎥⎦ (A.9)

where A1, A2, A3 and A4 are the coefficients yet to be determined. It should be noted that b and k arepredetermined variables. For the solution to be bounded we set A3 = A4 = 0. Hence, we can write thefollowing:

bt − b = �11A1e�1t + �21A2e�2t (A.10)

kt − k = �13A1e�1t + �23A2e�2t (A.11)

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Assuming that at time t = 0 we have b = b0 and k = k0, we can solve (A.10) and (A.11) for A1 and A2to obtain equations for the saddle path as follows:

bt − b = (b0 − b)(B1e�1t + B2e�2t) + (k0 − k)(B3e�1t + B4e�2t), (A.12)

kt − k = (b0 − b)(B5e�1t + B6e�2t) + (k0 − k)(B7e�1t + B8e�2t), (A.13)

t − = (b0 − b)(B9e�1t + B10e�2t) + (k0 − k)(B11e�1t + B12e�2t), (A.14)

qt − q = (b0 − b)(B13e�1t + B14e�2t) + (k0 − k)(B15e�1t + B16e�2t), (A.15)

where Bi is given asB1 = �11�23

�11�23−�13�21, B2 = −�21�13

�11�23−�13�21, B3 = −�11�21

�11�23−�13�21, B4 = �21�11

�11�23−�13�21, B5 = �23�13

�11�23−�13�21,

B6 = −�23�13�11�23−�13�21

, B7 = −�21�13�11�23−�13�21

, B8 = �23�11�11�23−�13�21

, B9 = �12�23�11�23−�13�21

, B10 = −�22�13�11�23−�13�21

,

B11 = −�11�21�11�23−�13�21

, B12 = �21�11�11�23−�13�21

, B13 = �14�23�11�23−�13�21

, B14 = −�24�13�11�23−�13�21

, B15 = −�21�14�11�23−�13�21

,

B16 = �24�11�11�23−�13�21

.

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dx.doi.org/10.1016/j.najef.2014.07.004

the real effects of inflation in a developing economy with external debt and sovereign risk

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