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

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North American Journal of Economics and Finance

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

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Q1 3 4

Mark Assibey-Yeboah a, Mohammed Mohsin b,∗ a b

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

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6

a r t i c l e

i n f o

a b s t r a c t

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

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JEL classification: E52 F32 F41 O40

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Keywords: Monetary policy Cash-in-advance External debt Risk premium

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1. Introduction

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In this paper we develop an intertemporal optimizing model to examine the real effects of inflation induced by monetary policy in an open developing economy with external debt and sovereign risk. The economy faces an upward sloping supply curve of debt. In our model, households require real balances in advance for consumption expenditures, and monetary policy involves targeting the inflation rate. We show that an increase in the inflation rate leads to a decrease in the stock of foreign debt. It also leads to a decrease in consumption, employment, capital accumulation and output in the long run. Our results show that the accumulation of foreign debt exhibits non-monotonic adjustment. Particularly, an increase in the inflation rate leads to a current account surplus followed by a deficit. Along with this non-monotonicity, our model also explains the positive correlation between savings and investment during the transitional periods (Feldstein–Horioka puzzle). © 2014 Published by Elsevier Inc.

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 by creating 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.2014.07.004 1062-9408/© 2014 Published by Elsevier Inc.

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as a means of keeping the rate of money growth in check. On top of the monetization, developing economies rely heavily on external borrowing to carry out their development programs. This leads to the accumulation of substantial external debts with its attendant cost of debt servicing. With a majority of the world’s population living in developing countries, it is important to understand and gauge the prospects of economic development by examining the effects of monetary policy in the face of the increasing reliance on external capital. In this paper we develop a neoclassical monetary growth model to examine the effects of inflation induced by domestic monetary policy in a small open developing economy with external debt and sovereign risk. A brief overview of the existing literature will adequately justify the need for this study. The neoclassical monetary growth models,1 on which we put a lot of emphasis, are known to produce conflicting results.2 First, Tobin (1965) argued that higher inflation is associated with higher capital 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. On the other hand, Stockman (1981), Abel (1985), Lucas and Stokey (1987), Dotsey and Sarte (2000) and others consider cash-in-advance (CIA) economies to show that inflation has a negative effect on output in the long-run.4 The open economy literature has always shown ample interest in the effects of monetary policy on output, employment and the current account. The seminal papers which consider policy issues in an optimizing framework are by Obstfeld (1981a, 1981b). In both papers, he uses the MIU framework and employ Uzawa type preferences and claims that though in the short-run higher inflation leads to lower level of consumption and demand for real balances, the economy in the longrun will experience current account surplus and higher level of consumption. It is important to note that Obstfeld (1981b) considers the policy effects for such an economy when the central bank fixes the rate of growth of money whereas Obstfeld (1981a) assumes that the central bank fixes the rate of devaluation of the domestic currency. Though the findings are very similar, the analysis is considerably simplified if one assumes that the central bank targets the rate of change of the exchange rate (or domestic inflation rate). It is also well known that the steady state policy effects are the same regardless 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 studies are limited on many grounds. First, as the model deals with an endowment economy, it precludes any discussion of the effects of monetary policy on employment, output, and investment. Second, the MIU 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 the empirical 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 implement inflation 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 price rigidities to generate frictions to provide non-neutral effects of monetary policies. The labor market does not necessarily clear at all times, hence, policymakers deal with actual and potential (full-employment) levels of output and employment. Policymakers also deal with actual inflation and inflation gaps. The monetary authority often follows Taylor-type rules to conduct monetary policies. For details, see Clarida, Gali, and Gertler (1999), Obstfeld and Rogoff (1995), Ida (2011) and Woodford (2003). Because of these fundamental modeling differences, the results of these new-Keynesian models are often different from the neoclassical monetary 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 inflation uncertainty lowers output growth, while the direct effect of average inflation on output is actually positive and significant for 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 with consumption, 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 bank may possibly be intervening in the foreign exchange market to some extent only during the adjustment period before the steady state. Also, as we will see, instead of intervening in the foreign exchange market the central bank could adjust the rate of growth of money appropriately.

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

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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 simplified their analysis by assuming that the central bank targets the domestic inflation rate and not the rate of growth of money. Along with labor/leisure choice and CIA constraint(s),7 the study shows that an unanticipated 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 consumption and investment dominate the fall in output. They also report that temporary changes in domestic inflation rates have permanent effects in the economy. These open economy monetary models too provide no clear-cut conclusions. Moreover, these studies 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 and sovereign risk. The risk that a borrower will default on a loan affects the market interest rate. The cost of borrowing is often an increasing function of the stock of debt. This observation was originally documented 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) to address different open economy macroeconomic issues. In this paper we will also incorporate this idea 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 also study 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 of instruments and targets in a small open economy within a new-Keynesian framework and Calvostyle nominal price rigidities. Specifically, Tuladhar compares a benchmark efficient markets model with a monetary targeting regime and three different inflation targeting rules (namely, Taylor type, CPI inflation, non-tradable inflation). As noted earlier, these modeling features differ fundamentally from that of our proposed model. In fact, our proposed model has more similarities with Assibey-Yeboah and Mohsin (2012). They proposed a simple model to support their empirical findings that inflation is negatively correlated with consumption, investment and the stock of foreign debt. They show an economy with inelastic labor supply and imperfect capital mobility supports those empirical findings if both households and firms hold real balances in advance for their expenditure.8 However, this model is limited as there is no labor/leisure choice for consumers, and it does not reflect employment effects of monetary policies. In addition, their model does not support the non-monotonic transitional dynamics of the current account that is often reported in the empirical literature. The proposed model will address these concerns. In our model households can make labor–leisure decisions. Firms produce output with labor and capital as inputs. Similar to Obstfeld (1981a), Calvo (1987), Mansoorian and Mohsin (2006) and many others, we assume that monetary policy is conducted by controlling inflation. Moreover, we adopt the CIA framework as it is more appropriate in developing economies, where the credit market is not well developed. 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 consumption relative to leisure, inducing the representative household to substitute leisure for consumption. The resulting 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 long run 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 that the rate of time preference is equal to the world rate of interest. This restriction, in fact, poses a serious limitation for studying the dynamic effects of government policies. To overcome this, Obstfeld used Uzawa type preferences. Here, the rate of time preference is an increasing function of instantaneous utility which was required for saddle point stability rather than for any economic 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 higher inflation 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 exercise reveals that even though capital decreases throughout the transitional period, the initial rate of decline of investment is higher than it is during the later part of the adjustment period. The initial fall in employment actually decreases the marginal productivity of capital. After the initial jump, employment continues falling for a while before it starts increasing to reach the new steady state. On the other hand, after its initial fall, consumption grows during the early transitional period before it starts declining again to reach its steady state level. We observe non-monotonic adjustment of the accumulation of foreign debt; initial decrease followed by gradual increase. Since the negative of foreign debt measures the current account position of the economy, we can claim that the current account balance of the economy exhibits a non-monotonic adjustment due to a permanent inflationary shock in the economy. During the initial transitional period the current account position improves, then deteriorates gradually. Interestingly, during the major part of the transitional period we observe a positive correlation between savings and investment (Feldstein–Horioka (1980) puzzle). Interestingly, previous open economy monetary growth models within the neoclassical setup could not support this stylized fact. The rest of the paper is organized as follows. The main model and its findings is presented in Section 2. Section 3 outlines the model with labor–leisure choice, and the concluding remarks are given in Section 4.

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2. The model

103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119

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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 by households, 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 = Et Pt∗ ,

(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 (≡ P˙ t /Pt ) is the domestic inflation rate, εt (≡ E˙ t /Et ) is the rate of change of the exchange rate, and t∗ (≡ P˙ t∗ /Pt∗ ) is the foreign inflation rate. We assume that the foreign price of the good is fixed at P∗ . With flexible prices, the change in the rate of inflation is equal to the rate of depreciation of the domestic currency (t = εt ). Unlike the standard assumption of perfect capital mobility where a small open economy can borrow at a fixed world interest rate, r∗ , we assume that a developing economy is required to pay an additional risk premium. The country-specific risk premium, Z, depends on debt-servicing ability. Thus, the effective interest rate for the economy, r˜t , is given as r˜t = 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 shows the stock of capital, and lt denotes labor supply. The possibility of a cutoff in debt is captured by the 141 Q2 assumption that the function Z(.) is convex (Z >0).10 We proceed by considering the problem facing 142 each sector in turns. 139 140

10 The country-specific risk premium, Z, is modeled differently in different studies. For example, Fisher (1995) and SchmittGrohe 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 the net foreign assets or the foreign capital flow. In our case, it depends on the economy’s creditworthiness captured by debtoutput ratio. Though we are not the first to introduce such debt-elastic interest rate, but to the best of our knowledge, we are incorporating this to offer a comprehensive monetary growth model of a developing economy within the neoclassical framework.

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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 , in order to maximize the present value of lifetime utility, U, as given by:



∞

U=

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u(ct, lt )e−ˇt dt,

(3)

0 148 149 150 151 152 153 154

where ˇ(> 0) is the fixed rate of time preference. For simplicity we assume that the utility function is additively 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 from consumption and leisure. In addition we assume that u(.) also satisfies lim u (.) = ∞. ct →0

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

155

(4)

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

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at = mt − bt.

157

(5)

His flow budget constraint is given by:

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a˙ t = Dt + wt lt + t − r˜t bt − ct − t mt ,

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(6)

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where Dt is the total dividend received by the representative household, wt is the real wage rate and t mt is the “inflation tax” on real balances. Eq. (6) implies that the agent will accumulate assets to the extent 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,

164

a(0) = a0 . The agent must also satisfy the No-Ponzi game condition lim at e

160 161 162

t

t→∞

165 166

169 170

r˜s ds

 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 + wt lt + t + r˜t at − (1 + r˜t + t )ct ].

167 168

o

(7)

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



bt f (kt , lt )





U  (ct ) = t

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V  (lt ) = −t wt ,

(8b)

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˙ t = t ˇ − r˜t ,

(8c)

174



1 + r∗ + Z



171

+ t

,

(8a)



and the standard transversality condition lim t at = 0. Eq. (8a) equates the household’s marginal cost t→∞

175 176 177

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

M

B

To see how (6) is derived note that mt = P t and bt = P t = Pt , where Pt is price level, PBt is nominal unit price of foreign t t t debt 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 ˙t M B˙ P˙ ˙t= − t mt and b˙ t = t − t bt , where the rate of inflation t = t . Incorporating real debt (in terms of repayment). Hence m 11

Pt

Pt

Pt

˙ t − B˙ t = Pt (Dt + wt lt ) − it Bt + Pt t one obtains these results into the representative agent’s nominal budget constraint Pt ct + M Eq. (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 production function 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 fkk fll − fkl2 = 0. Investment involves adjustment costs given by the function: ˚(It ) = It +  (It ),

where ˚(It ) is the total cost associated with the purchase of It units of new capital, and  (It ) are the adjustment costs associated with It . The function  (It ) is assumed to be a nonnegative, convex function, with ˚ ≥ 0; ˚ > 0. In addition, we may set  (0) = 0 and   (0) = 0, which means that the cost of zero investment is zero, ˚(0) = 0 and the marginal cost of initial investment is unity, ˚ (0) = 1. The dividend payment net of investment expenditure is Dt = f (kt , lt ) − wt lt − ˚(It ).



∞

Dt e

−

t 0

r˜v dv



dt =

0

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(10)

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

191

192

(9)

∞

[f (kt , lt ) − wt lt − ˚(It )]e

−

t 0

r˜v dv

dt,

(11)

0

subject to: k˙ t = 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 ) − wt lt − ˚(It ) + qt It ,

(13)

where qt , the co-state variable associated with the state variable kt , is the shadow price of capital. The first-order optimality conditions for this problem with respect to lt , It , and kt are, respectively: fl (kt , lt ) = wt ,

(14a)



200

˚ (It ) = qt ,

(14b)

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q˙ t = qt r˜t − fk (kt , lt ),

(14c)

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and the transversality condition lim qt kt = 0. t→∞

203

204 205 206 207 208 209 210 211 212 213 214 215 216 217 218

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

(15)

Eq. (15) implies that government expenditure, which consists of real monetary transfers  t should ˙ t + t mt ). As outlined earlier, we assume be equal to total government revenues from seigniorage (m Please cite this article in press as: Assibey-Yeboah, M., & Mohsin, M. The real effects of inflation in a developing economy with external debt and sovereign risk. North American Journal of Economics and Finance (2014), http://dx.doi.org/10.1016/j.najef.2014.07.004

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that the central bank targets the inflation rate (t ), by continuously adjusting the transfers  t . This is very 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 simply controls the growth rate of money supply and as a result the inflation rate becomes endogenous and variable off the steady state. This then increases the dimension of the dynamic system. By assuming inflation 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 system would 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 state effects, there is no approximation error. It well known (and can be shown easily) that the steady state policy effects are the same, regardless of whether the central bank fixes the rate of growth of money or the inflation rate.

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2.4. Equilibrium dynamics

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



235

U  (ct ) = t 1 + r ∗ + Z

236

V  (lt ) = −t fl (kt , lt ),

237

˙ t = t ˇ − r ∗ − Z

238

˚ (It ) = qt ,

239

q˙ t = qt r ∗ + Z

240

k˙ t = It ,

241

242 243







b˙ t = r ∗ + Z









bt f (kt , lt )

bt f (kt , lt )

bt f (kt , lt )

bt f (kt , lt )









+ t ,

(16a) (16b)

 ,

(16c) (16d)

− fk (kt , lt ),

(16e) (16f)

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 be represented by the following equations:

244

ct = c(t , kt , t , bt ),

(17a)

245

lt = l(t , kt ),

(17b)

246

It = I(qt ).

(17c)

247 248 249

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





bt f (kt , l(t , kt ))

250

b˙ t = r ∗ + Z

251

˙ t = t ˇ − r ∗ − Z

252

k˙ t = I(qt ),

253

q˙ t = qt r ∗ + Z



254 255









bt + c(t , kt , t , bt ) + ˚(I(qt )) − f (k, l(t , kt )),

bt f (kt , l(t , kt ))

bt f (kt , l(t , kt ))



(18a)

 ,

(18b) (18c)

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

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two negative and two positive eigenvalues. The details of the linearized system is outlined in the Appendix. It is important to highlight the role of investment adjustment costs in this model. In general, in a model with adjustment costs, capital adjusts slowly and does not make a discrete jump (like a control variable) at the time of policy changes. It also reduces the volatility of investment. However, in our model, adjustment costs play a bigger role. For better exposition, let us assume that we do not have any adjustment costs function. Following, from the firm’s problem, we will have qt = 1 in Eq. (14b) and r˜t = fk (kt , lt ) in Eq. (14c). Recall that these are not steady state conditions, but rather must hold true at all times. The transitional dynamics between k and q will thus collapse as investment will not be a function of q (see Eq. (16d) or (18c)). In such a setup, capital will discretely adjust to steady state and display no transitional dynamics. The system will have only one negative eigenvalue and there will be the absence of non-monotonic adjustment of the current account and other variables.

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2.5. The effects of inflation

256 257 258 259 260 261 262 263 264 265 266 267

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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 inflation rate. At the steady state we must have ˙ = q˙ = k˙ = b˙ = 0. Thus, any variable xt is represented by x in steady state. The steady state is captured by the following equations:



U  (c) = t



1 + r∗ + Z

f (k, l)



275

V  l = −fl (k, l),



276

ˇ = r∗ + Z

278

fk (k, l) = r ∗ + Z



281 282 283 284

(19a) (19b) (19c)

b



(19d)



f (k, l)

f (k, l) = r ∗ + Z

,



b

qt = 1,

280



+

f (k, l)

277

279



b

b f (k, l)

,

(19e)

 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 the shadow price of capital q. The steady state effects of an increase in inflation, obtained by differentiating the long-run equilibrium, i.e. Eqs. (19a)–(19f) with respect to  are as follows:

285

f {(f f − fl fkk )(f − r˜ b)} dc = l k kl < 0, d 

(20)

286

dq = 0, d

(21)

287

dk f f f = kl l < 0, d 

(22)

288

dl f f f = − kk l < 0, d 

(23)

289

b(−flk fk fl + fl2 fkk ) db < 0, =−  d

(24)

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f fV d = kk d 

9



< 0,

(25) 



where  = U (f − r˜ b)(flk fk fl − fkk fl2 ) − (1 + r˜ + )fkk fV < 0. The steady state effects show that an increase in the inflation rate reduces the long-run marginal utility of wealth, debt, labor supply, and consumption. The intuition behind these results are given as follows. 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 terms of 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 productivity of 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 dk dl = fk + fl < 0. d d d

(26)

306

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

307

2.6. A numerical evaluation

301 302 303 304 305

320

In this section we perform a detailed numerical evaluation of our model. This is important for many reasons. First, because of the complex nature of the model, we are unable to show analytically that the model has saddle point stability. With reasonable functional forms and parameter values, we can numerically 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 cannot obtain simple phase diagrams as well as the optimal paths (transitional dynamics) of all the major variables easily. A numerical evaluation will help us immensely in this regard. Third, we can easily perform sensitivity analysis for different parameter values to evaluate the effectiveness of monetary policy. Finally, it should also be noted that the real purpose of this calibration exercise is not intended to match the real world data, rather that it aims at providing further insights into the qualitative behavior of economic variables subject to reasonable bounds. To begin, we specify functional forms for the production function, utility function and the upward sloping supply curve of debt. Following the Real Business Cycle (RBC) literature, we assume that the

321

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

322

production function is Cobb Douglas, y = k l1− . The functional form of the upward sloping supply

308 309 310 311 312 313 314 315 316 317 318 319

323 324 325 326 327 328

a

(c 1−˛ (1−l)˛ ) 1−

1−

−1

, and the

b

curve of debt is specified as r˜ = r ∗ + e f (k,l) − 1 (see Chatterjee & Turnovsky, 2007). Following Cooley and 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, ˇ = 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, we substitute 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, where the 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 steady nor deccumulation of foreign debt. It will be clearer, further, once state, the economy will neither experience  accumulation 

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

b f (k,l)

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

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

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L

L1 L2 L0

0

t

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

b

b1 b2

0

t

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

329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351

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%. Capital stock and employment both decrease by 2.02 percent. As a result of this inflationary shock, output also decreases by 2.02 percent. At the same time we observe a 2.02 percent decline in the stock of foreign debt. It should be recalled that at the steady state the rate of time preference (which is fixed by assumption) should be equal to the effective interest rate faced by the economy. This means that the risk premium in both equilibria must be the same (4% in this example), which can only be obtained if both debt and output change proportionately. As part of our numerical exercise, we calculate the short run effects too. At t = 0 when the inflationary shock is implemented, there are no short run effects on the stock of debt and the level of capital as both of them are predetermined variables. Consumption initially declines from 0.86 to 0.85, a 1.10 percent decrease. 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 level of 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 increase in inflation. The transitional dynamics following the increase in  are derived from the linearized system and are given in the Appendix. In this economy, an increase in the inflation rate makes consumption more expensive (in terms of leisure). Households respond by reducing consumption of goods and increasing the consumption of leisure. Labor supply in the short run goes down as a result. Though in the short run capital does not change, output level will decrease due to lower employment. The lower level of employment decreases the marginal productivity of capital and hence investment starts declining. As a result the capital stock starts falling. After the initial fall, consumption continues to Please cite this article in press as: Assibey-Yeboah, M., & Mohsin, M. The real effects of inflation in a developing economy with external debt and sovereign risk. North American Journal of Economics and Finance (2014), http://dx.doi.org/10.1016/j.najef.2014.07.004

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11

c c1 c0 c2

0

t

Fig. 3. Time path of consumption.

k

k1

k2

0

t

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

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increase during the early transitional periods before it starts declining again. The detailed adjustment path of consumption is outlined in Fig. 3. The adjustments of other major variables are non-monotonic as well. Our numerical exercise reveals that after an immediate downward jump, employment keeps dropping for a while and then gradually increases to reach its new steady state level (see Fig. 1). On the other hand, capital stock decreases throughout the transitional period. However, the initial rate of disinvestment is higher than it 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 the economy leads to a lower level of foreign debt in the long run in real terms. This means that during the transitional period the economy repays some of its outstanding foreign debt. Moreover, this process is non-monotonic. Its detailed adjustment path is given in Fig. 2. Our numerical exercise reveals that the economy deccumulates foreign debt during the very early phase of the adjustment process. After a short while, the economy starts accumulating debt again. The economic intuition is very clear. It should be noted that debt and capital are predetermined variables. In the short run, due to an decrease in employment, the output level goes down. As a result, the economy worsens its creditworthiness instantly. With a higher effective cost of borrowing, it is not surprising that the economy starts to borrow less. However, the effective interest rate will adjust gradually towards its long run level and hence 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 further clarity. Now, if we focus our analysis in terms of current account adjustment, it means the current account position of the economy exhibits a non-monotonic adjustment as well. During the initial transitional period, the current account position improves, then it subsequently decreases. So during the major part of the transitional period, our model explains the positive correlation between savings and investment – Feldstein–Horioka (1980) puzzle. For more discussions on the Feldstein–Horioka Please cite this article in press as: Assibey-Yeboah, M., & Mohsin, M. The real effects of inflation in a developing economy with external debt and sovereign risk. North American Journal of Economics and Finance (2014), http://dx.doi.org/10.1016/j.najef.2014.07.004

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398

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 open economy and our modeling features have much in common, it will be relevant to look into the dynamic adjustment of the macroeconomic variables in their study and compare it with our findings. Such comparison will also highlight the role of the country-specific risk premium that is playing in our model. In both models we find steady state decreases in investment, employment, output and consumption. This is not surprising, though, as in both models CIA constraints play a similar role. Though in both models the steady state effects on the net asset position is the same, the underlying reasons are significantly different. The decreased debt position in our model is attributed to the upward sloping supply curve of debt (or risk premium) we deploy whereas in Mansoorian and Mohsin the result is attributable to the imposed 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 and as a result the transitional dynamics are also significantly different. For example, if we were to assume a separable preference in their model (as in our case) the transitional dynamics involving consumption will be significantly different. In that case, consumption depends on both the marginal utility of wealth and inflation, and takes a discrete jump to reach a new steady state given any external inflationary shocks. In other words, due to ‘zero-root’ problem, consumption does not exhibit any transitional dynamics. More importantly, due to non-monotonic adjustment of the current account, our model could 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 could overcome this limitation.

399

3. The model without labor/leisure choice

376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397

400 401 402

403

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 this fixed employment economy:





b˙ t = r ∗ + Z



˙ t = t ˇ − r − Z k˙ t = I(qt ),

406

q˙ t = qt r ∗ + Z

408 409 410 411 412 413

414





416

,

(27b) (27c)



bt

− fk (kt , l).

(27d)

We could easily linearize the above system as we did in (A.8) in the appendix to demonstrate that the model has saddle point stability. Once again, the system has two predetermined variables (b and k) and two jump variables ( and q). For saddle point stability the coefficient matrix of the linearized system must have two negative and two positive eigenvalues. In this special case we can easily prove that the system is saddle point stable. Now we examine the impact of an unanticipated and permanent increase in the inflation rate on steady state levels of the variables. The steady state is captured by the following equations:



U  (c) = 



1 + r∗ + Z

415

f (kt , l)

f (kt , l)

(27a)



bt

∗

405

407

bt + c(t , bt , kt , t ) + ˚(I(qt )) − f (kt , l),

f (kt , l)

404



bt

ˇ = r∗ + Z q = 1,

b f (k)



b f (k)





+

,

(28a)

(28b) (28c)

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417

fk (k) = r ∗ + Z

418

b



f (k)



f (k) = r ∗ + Z

13

b f (k)

,

(28d)

 b + c.

(28e)

431

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

432

4. Concluding remarks

419 420 421 422 423 424 425 426 427 428 429 430

446

In this paper, we study the dynamic macroeconomic effects of monetary policy aimed at targeting inflation rate. We consider a small open economy with an external debt and sovereign risk – a typical developing economy. Our economy faces an upward sloping supply curve of debt as well. Households hold 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 increase in inflation rate lowers the level of investment, employment, production and consumption in the long run. However, the economy could lower its level of foreign debt. All the major variables exhibit non-monotonic transitional dynamics. Interestingly, our model is capable of explaining the positive correlation 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 deterministic in nature. As a result, we are not able to evaluate the effects of monetary policy when the economy is subject to other shocks like productivity shocks and shocks involving foreign interest rates and terms of trade. To adequately address these concerns one needs to adopt a dynamic stochastic general equilibrium (DSGE) framework. Unfortunately, that is beyond the scope of this paper.

447

Uncited references

433 434 435 436 437 438 439 440 441 442 443 444 445

448

449

Q3

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

451

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

452

Appendix A. Equilibrium dynamics

450

453

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

454

ct = c(, k, , b),

(A.1)

455

lt = l(, k),

(A.2)

456

It = I(q),

(A.3)

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with the corresponding partial derivatives: c = −

Z  bf 

k

U f2

> 0, l = −

fl  V (l)+fll





462

˙ =  ˇ − r ∗ − Z

463

k˙ = I(q),



q˙ = q r ∗ + Z

⎡





b f (k, l(, k))

a11

a12

a41

a11 =



a13

cb + r˜ +

bZ  f

469

a14 = Iq , a21 = − Zf , a22 =

470

a43 = −



474 475 476 477 478 479 480



qZ  b (fk f2

bt − b

483 484

(A.4)

 ,

(A.5)

− fk (k, l(, k)).

(A.7)

⎤

q−q

a44







a12 = c − 1 +

,

Z  bf l l , f2



(A.8)

a23 =

Z  b (fk f2

b2 Z  f2



fl l ,





a13 = ck − 1 +

+ fl lk ), a34 = Iq , a41 =

qZ  , f

a42 = −

b2 Z  f2







(fk + fl lk ) ,

qZ  bf l l f2



+ fkl l ,

+ fl lk ) + (fkk + fkl lk) , and a44 = ˇ.

⎤

⎡

11

21

31

41

⎤⎡

A1 e1 t

⎤

⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ t − ⎥ ⎢ 12 22 32 42 ⎥ ⎢ A2 e2 t ⎥ ⎢ ⎥=⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎣ kt − k ⎦ ⎣ 13 23 33 43 ⎦ ⎣ A3 e3 t ⎦ qt − q

482

> 0.

All elements of the coefficient matrix in (A.8) are evaluated at their steady state values. The system has two predetermined variables (b and k) and two jump variables ( and q). For saddle point stability the coefficient matrix must have two negative and two positive eigenvalues. Because of the complexity of the model, it is not possible to show saddlepoint stability analytically. Our numerical exercise, however, shows that the conditions for saddlepoint stability will be satisfied with reasonable functional forms and parameter values. Moreover, as a special case (in the model with inelastic labor supply) 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  1 and  2 are negative, while  3 and  4 are positive. Also, suppose ( i1 , i2 , i3 , i4 ) is the eigenvector associated with  i , ∀ i = 1, 2, 3, 4. Then we can write

⎡

481



a14

a43

a42

where

473

< 0, ck =

b + c(, b, k, ) + ˚(I(q)) − f (k, l(, k)),

b f (k, l(, k))

468

472

Z   fU (c)

⎡ ⎤ ⎢ ⎥ b−b a a 0 ⎥⎢ − ⎥ ⎢a ⎥⎢ ⎢ ⎥ = ⎢ 21 22 23 ⎥, ⎥ ⎣ k˙ ⎦ ⎢ 0 0 0 a34 ⎦ ⎣ k − k ⎦ ⎣ b ⎢ ˙ ⎥ q˙

471

1  ˚

< 0, cb =

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

⎡˙⎤ 467

> 0, and Iq =

  U (c)

(A.6)



466



b f (k, l(, k))

b˙ = r ∗ + Z

465

flk  V (l)+fll

=

The dynamic behavior of the economy is determined by the following system of differential equations:

461

464

> 0, lk = −

f 2 [1+˜r +]−Z  bf l l , c  f 2 U (c)

14

24

34

44

(A.9)

A4 e4 t

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

485

bt − b = 11 A1 e1 t + 21 A2 e2 t

(A.10)

486

kt − k = 13 A1 e1 t + 23 A2 e2 t

(A.11)

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498

499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546

15

Assuming that at time t = 0 we have b = b0 and k = k0 , we can solve (A.10) and (A.11) for A1 and A2 to obtain equations for the saddle path as follows: bt − b = (b0 − b)(B1 e1 t + B2 e2 t ) + (k0 − k)(B3 e1 t + B4 e2 t ),

(A.12)

2 t

(A.13)

kt − k = (b0 − b)(B5 e

1 t

t − = (b0 − b)(B9 e qt − q = (b0 − b)(B13 e

1 t

where Bi is given as B1 = 11− 23 , B2 = 11 23

13 21

− 13 , B6 = 23 11 23 − 13 21 − 21 B11 = 11 , 11 23 − 13 21 B16 = 24− 11 . 11 23 13 21

+ B6 e

1 t

+ B10 e + B14 e

) + (k0 − k)(B7 e

2 t

2 t

1 t

+ B8 e

) + (k0 − k)(B11 e ) + (k0 − k)(B15 e

1 t

1 t

2 t

), 2 t

),

(A.14)

2 t

),

(A.15)

+ B12 e + B16 e

− 21 13 − 11 21 11 23 − 13 21 , B3 = 11 23 − 13 21 , − 21 13 23 11 B7 = − , B8 = − , 13 21 13 21 11 23 11 23 B12 = 21− 11 , B13 = 14− 23 , 11 23 13 21 11 23 13 21

21 11 11 23 − 13 21 , 12 23 B9 = − , 13 21 11 23 − 13 B14 = 24 , 11 23 − 13 21

B4 =

B5 = B10 = B15 =

23 13 11 23 − 13 21 , − 22 13 11 23 − 13 21 , − 21 14 11 23 − 13 21 ,

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