Poverty traps: instabilities do matter

Poverty traps: instabilities do matter Vincent GERONIMI ECONOMIX, University Paris 10, France Laurent MATHIEU ECONOMIX, University Paris 10, France Patrick SCHEMBRI C3ED, University Versailles St Quentin en Yvelines, France Armand TARANCO University Aix-Marseille, France March 12, 2006

Abstract This paper investigates both empirical aspects and theoretical mechanisms that support the poverty trap view for Sub Saharan Africa countries. The controversies about stylised facts of poverty traps are revisited in the …rst part of this contribution. Whereas long-term instability of growth appears as a virtually universal feature of trapped countries, it remains largely unexplained in the literature. We therefore draw special attention to the link between shocks (such as instabilities in time series commodity prices) and low growth of Sub Saharan African countries. The second part of this contribution presents a macroeconomic model to explore the links between instabilities and poverty trap. With a complementary a¤ecting global returns, the modi…ed standard optimal growth model (Collier and Gunning, 1995) used for the analysis of shocks management leads to multiple equilibriums. One striking result of this model is that the standard policy of sterilisation of positive external shocks can lock an economy in a poverty trap. This is a situation where instabilities do matter in long run dynamics. It has strong policy implications for African trapped countries. Keywords: Poverty traps - optimal growth model JEL classi…cation: O11, O47

Corresponding author. email: [email protected]

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1

Introduction

The analysis of poverty traps in which developing countries would be stuck do know a renewed attraction, both on theoretical and empirical grounds. Thus, Azariadis and Stachurski [2004] in their article make an exhaustive review of the literature on the subject putting forward the theoretical explanatory factors contributing to the existence of a poverty trap. In the same way, Sachs [2004] advocates for a "big push" to escape from poverty traps. Moreover, recent UN’s overview report about Millenium Project [2005] echoes Sachs’ conclusions as one reads: "...Tropical africa even in well governed parts is stuck in a poverty trap, too poor to achieve an high level of economic growth, and in many places simply too poor to grow at all...(Chap 10) ...Consistent with the poverty maps, countries should undertake a needs assessment to identify the speci…c public investments necessary to achieve the goal, including faster overall economic growth supported by major public investments in infrastructure and private sector promotion" (chap 17) Eventually, even IMF and World Bank in their "Global Monitoring Report" in 2005 conclude with the need of a big push for the developing countries to escape the poverty trap: "...O¢ cial development assistance must at least double in the next …ve years to support the MDGs, particularly in low-income countries and Sub-Saharan Africa" Nevertheless, the question of the existence of poverty traps is not a new one, as one …nds it in the early writings on development economics. Thus, the need of a "Big Push" allowing the Eastern European Industry to emerge is found in Rosenstein Rodan. In the same way, the "Take o¤" is found in the well known Rostow’s book "Stages of Economic Growth". However, even the existence of poverty trap with its corollaries -Big Push and Take o¤- appears to be disputed by some authors. The more emblematic one is Easterly [2005] who in its critical assessment of the – poverty trap / big-push / take-o¤ –narrative rejects the poverty trap hypothesis following two lines of argumentation: 1-There are very few zero growth (of per capita income) countries over the whole period 1950-2000; 2-Log per capita incomes are not stationary. Concerning the …rst point, the "zero growth" speci…cation of poverty traps con…guration seems very restrictive. . . Easterly himself soften this condition in the second part of its paper where the growth lays in the [-0.5; 0.5] interval. Moreover, a relative de…nition of poverty traps (growth signi…cantly weaker for trapped countries) leads to the opposite conclusion considering the whole period 1961-2000 (and for the 1985-2001 period as stated by Easterly). Its 2

empirical statement that there are no general poverty traps con…gurations is highly dependent upon its choice over the period and sub-period as well as the grouping of countries. The second empirical statement, "log per capita incomes are non stationnary", is highly coherent with the fact we emphasise below, which is the existence of an inverted relation between volatility in the output and output growth. Indeed, if poverty traps exist they are not of the “macro inertia” kind. High instability of growth, and low persistence in output growth, has been widely analysed in the literature (e.g. Easterly and alii [1993], Acemoglu and Zilibotti [1997], Easterly and Levine [2002]). SSA countries have experienced several structural breaks over the 1960-2000 period, a …nding that di¤erentiate strongly developing countries from developed countries, most of the latter having experienced no break at all since the end of world war II. Poverty traps skepticism seems to be justi…ed by the contradictions between the conclusions of theoretical models and stylised facts. On one side, Azariadis and Stachurski [2004] underline that in standard neoclassical models, poverty trap is de…ned by opposite equilibrium, low level to a higher one. In this context, low growth is linked to limited ‡uctuations of per capita growth rates (an “inertia hypothesis”). As noted by the authors (pp. 27): “Under our assumption of unbounded shocks there is always the potential –however small- to escape any basin of attraction. So in the long run initial conditions do not matter” Thus, instabilities (considered here as a succession of exogenous shocks) may overcome initial di¤erences and lead to convergence, pulling economies out of macroeconomic poverty traps. As a consequence, with non convex technology, low level of instability (“low noise”) is associated with low equilibrium. Near the steady state “the growth rate would just represent ‡uctuations around a steady state income” (Easterly and alii [1993]). Thus, high instability of the GDP per capita growth rate is associated with “take-o¤”. On the other side, the macroeconomic “inertia”of poverty traps featured in these models is not consistent with empirical evidence. Since Barro [1991] introduced a dummy variable for SSA countries in its analysis of the factors of international growth, several studies have attempted to explain the weak performance of these economies the main symptom being a limited GDP per capita together with a low growth rate of per capita GDP over a signi…cant period of time (a 1% loss in per capita growth rate compared to other countries according to Barro). A symptom which in turn leads to a growing proportion of people living with less than 1 dollar per day1 . A wide array of factors have been successively emphasized in this literature as the main explanation of this divergence between economies –from lack of human capital to lack of social capital, through bad institutions, bad governance and con‡icts 1 From 163.6 in 1981 to 312.7 million of people in 2001 in SSA countries (source Chen and Ravallion [2004] Table 4)

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(e.g. Collier [1999]. At the global level, none of these factors alone explain the empirical evidence of low GDP per capita growth rates and high instability of these rates. For SSA countries, instability of growth is mainly due to large exogenous shocks, external or internal, related to commodity price ‡uctuations, con‡icts, or climate changes. All these shocks are far from being of a white noise kind. Most of commodity prices shocks have a weak transitory component, and series of prices exhibit multiple structural breaks (Géronimi, Mathieu, Taranco [2003]). From a time series analysis perspective, climate ‡uctuations and con‡icts appear also as structural breaks. On the basis of this contradiction between theory and empirics over macroeconomic poverty traps, we address two questions in this paper. The …rst question is about the empirical link between macroeconomic volatility (as measured by standard deviation of output growth) and the output growth. In the next section, our study documents that among the developing countries, SSA countries are a strong example of the negative correlation between volatility of output and output growth since the region had known over the past fourty years the slowest output growth with the highest volatility. This empirical link comes into contradiction with neo classical models who concluded in the minor impact of volatility on growth and welfare. Moreover it reinforces the idea that SSA countries remain to a large extent stuck in poverty traps because of the instabilities mentionned above. Should there be a stylised fact of poverty traps to be stated concerning instability, it would be a high degree of instability rather than macroeconomic “inertia”. The second question we address concern the theoretical link between mediumterm shocks and poverty trap. In the last section we build upon a modi…ed standard optimal growth model (Collier and Gunning [1995]) to show that poverty traps situation can be a consequence of shocks. In this model which features an endogenous (structural) instability, even a temporary positive endogenous shock may lead to a lower equilibrium.

2

Data sets and stylised facts

In this section we …rst present the data used in the empirical analysis. After a discussion of the main properties of instabilites and shocks for SSA growth, we describe some stylised factsconcerning the link between output growth and instability. We …rst use standard statistical de…nitions of volatility to characterize instabilities in the growth rates. Then we turn to an analysis of dispersion of growth rates in the phase space to capture more exhaustively the dynamic properties of these instabilities. Data sets In the descriptive analysis that follows, we use the data set coming from the World Penn Tables ( Heston et al. [2002]). The data are annual and span the period 1960-2000. We consider a sample of 80 countries: 21 high income countries, 21 emerging countries and 33 Sub Saharian African countries.

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The former group is a subsample of OECD economies. The second group is considered as More Financially Integrated Economies according to Kose et al. [2003]. The third group comprises all the SSA countries less four countries for which no data were avalaible (Djibouti, Soudan, Erythre and Swaziland). To measure the output growth we use the per capita real GDP series. We calculate the medians for each group of countries on the full sample and the subsamples corresponding to decades. Traditionally (e.g. Ramey and Ramey [1995]) the macroeconomic volatility is measured by considering an indicator of output volatility: the standard deviation of per capita GDP growth which median is calculated on each group of countries. But this volatility measure, as all descriptive statistics assumes a smooth growth process with no sharp upward or downward trend to deliver an unbiaised message. This is not what we observe for SSA countries. So we consider a second volatility measure as proposed in Hnatkovska et al. [2003]. Using the band-pass …lter proposed by Baxter and King [1999] we estimate the trend of the per capita real GDP for each series.Then we compute the standard deviation of the output gap series which is the di¤erence between the real GDP series and the trend GDP. Table 1 compares the volatility in per capita real GDP for the three group of countries, using the two measures of volatility. We observe two common characteristics to the SSA countries compare to high income countries and other developing countries. Firstly, the divergence in the macroeconomic performances as measured by output growth between SSA countries and the other group countries is deep, getting even more accentuated the last two decades. This means that economic conditions allowing to increase the standard level of life of the populations are not met in these countries: more people live below the 1$ line of extreme poverty. This result moderates the …ndings of Easterly [2005]. Secondly, SSA countries do know a high degree of instability in output growth, about 3 times the ones of industrialised countries and 1.5 times the other developing countries. This result applies on the whole sample as well as the sub-samples with an increase during the 70’s corresponding to the shocks in commodity prices and a decrease in the 90’s below the level observed in the calm 60’s. Insert Table 1 We computed too a rolling volatility using the standard deviation measure over a 5 years rolling window to insure that the average measures on the whole sample as the cut into decades did not in‡uence the results. We represent this moving volatility in Figure 1. Insert Figure 1 We conclude this descriptive section by presenting the cross-countries relation between output growth and volatility in …gure 2. As observed, there is a negative correlation between output growth and volatility of growth for SSA countries. 5

Insert Figure 2 We propose in the following part an exploratory analysis of the dynamics of international growth rates which gives additional support to this inverted relation between growth and instability of growth. Growth and instability: an explanatory analysis of international growth dynamics As we underlined in the introduction, one of the most characteristic stylised facts of countries stuck in poverty traps is the high instability in their growth rates. Through an exploratory analysis of the dynamics of international growth rates (Annex, Box n 1) we …nd some additional empirical support to this alternative hypothesis (Annex, …gures 3, 4, 5, 6). The phase diagram of delayed growth illustrates the high dispersion of SSA growth together with its lower performance over the 1961-2000 period. The con…dence ellipses drawn for some SSA countries, USA and France clearly demonstrate the higher dispersion of the former compared to the latter, together with a lower rate of growth. Insert Figure2 3 The same ellipses drawn across all SSA countries and years reinforce the above conclusion: the mean performance is lower and dispersion is higher for SSA countries Insert Figure 4 Moreover, most SSA countries with poor economic performance over the last 40 years appear to share a high degree of instability compared to the rest of the world. Following the criteria of performance and instability those countries are signi…cantly di¤erent. In the dispersion-distance dimensions, SSA countries are di¤erent from other countries Insert Figure3 5 A cluster analysis di¤erentiates three clusters, the “stability and growth” cluster grouping almost all developed countries and only two African countries (Botswana and Mauritius). All other SSA countries are distributed between an “instability” cluster and a “instability and stagnation” cluster (Annex for the descriptive statistics of clusters). Insert Figure4 6 2 Source: Authors calculation from PWT 6.2, using GRGDPCH variable, real GDP per capita growth rate. Note : The ellipse, for a given value of , describes the area in which a single new observation can be expected to fall with a certain probability (95%), given that the new observation comes from a bivariate normal distribution with the parameters (means, standard deviations, covariance) as estimated from the observed points shown in the plot. 3 Source: Authors calculation from PWT 6.2, using GRGDPCH variable. Note : a = 70% 4 Source: Authors calculation from PWT 6.2, using GRGDPCH variable.

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Eventually, this …nding is highly consistent with the literature analysing factors of SSA poor performance. Persistence of shocks to commodity prices As shown in table 2, all the countries in SSA continue to rely on a narrow range of one to three commodities for the essential ot their export earnings. Insert Table 2 Indeed the instability in commodity prices, as measured by unit root or persistence tests adversly a¤ects output growth. Insert Table 3 Thus, these instabilities are far from the usual distribution of shocks incorporated into calculation of dynamics in the poverty traps literature (Azariadis and Stachurski [2004, p.32]). Rather than being short term ‡uctuations, SSA growth rates instability mirrors medium-term shocks, with strong dynamic implications. Con‡icts, climatic ‡uctuations, high dependency over concentrated primary exports, all are factors explaining growth rates instability. Though, poverty traps macroeconomic theory doesn’t take into account the fact that high level of instability works with low growth. How to reconcile theory and empirics over macroeconomic poverty traps instability? In order to reconcile theory and empirics over macroeconomics of poverty traps it is useful to go back to the initial analysis of poverty traps. From Rosenstein-Rodan [1943] to Nurkse [1953] and Scitovsky [1954] the “complementarity of investment activities across industries” is emphasized as a key element of development process. Spillovers may explain increasing returns depending upon the proportion of investment devoted to the same activities. If these spillovers are strong enough, non convexity can lead to multiple equilibrium con…guration, with a low and a high level equilibrium both stables. When trapped in the low equilibrium, market forces by itself won’t drive the economy to the better one. Modern theory analyses such poverty traps as the result of coordination failures (Ho¤ [2001]). Those spillovers are central to the construction of a macroeconomic model exhibiting the growth –instabilities properties found on empirical grounds. They are non-linear because they don’t play uniformly in the development process, with thresholds. Thus, spillover e¤ects are crucial in critical zones. With strong complementarity between infrastructure capital and private production, the capital rate of return will be a¤ected by the distribution of investment over time and sectors. Through this channel temporary shocks can have long-lasting e¤ects on the economy. Note : we use hierarchical forward clustering to identify homogeneous subgroups of countries. We choose Ward Method as linkage rule and squared euclidean distance as distance. In this methods cluster membership is assessed by calculating the total sum of squared deviations from the mean of a cluster. The criterion for fusion is that it should produce the smallest possible increase in the error sum of squares. This is an ANOVA-type approach.

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Assuming this complementarity, there is a macroeconomic channel from external shocks to growth. We have emphasised in previous studies (Géronimi, Schembri, Taranco [2002]) that a primary commodity specialisation meant a high degree of instabilities which could led to low growth. For most SSA countries exporting primary commodities, there is high concentration of exports on few primary commodities (commodity prices’‡uctuations have a strong impact on export earnings). These export earnings in turn constitute an essential source of government income, and public investment is highly correlated to government income. Thus, external shocks (e.g. commodity prices ‡uctuations) have a direct e¤ect over returns to capital through the complementarity e¤ect of public capital. An optimisation model, based on Collier and Gunning [1995], featuring those spillovers and complementary e¤ects, is discussed in the next section. It demonstrates that poverty traps situation can be a consequence of shocks.

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The Model

Assuming that these spillovers reveal their forces in a non-linear way and can generate multiple equilibria, we argue in this paper that: spillovers do not play their role uniformely in the development process, even though their e¤ects can be limited by productivity constraints affecting capital. They are characterised by thresholds. Spillover e¤ects can be signi…cant in critical zones where they can lead to higher development stages or poverty traps. There is a strong complementarity between infrastructure capital and private production. This complementarity is attached to the capital-share parameter and thus a¤ects the rate of return to capital. The individuals have to choose the timing and the volume of durable-goods purchases over time. This constraint can lead to large intertemporal substitutions and make economic outcomes subject to path dependence. In other words, temporary shocks can have long-lasting e¤ects on the economy. These ideas will be illustrated with an optimisation model, based on Collier & Gunning [1995]. The model describes the problem faced by a small open economy which has to adjust to a temporary positive trade shock, a primary commodity boom. Consider the following optimisation problem: Z 1 max W = e t u (c) dt t=0

k

= q

k

c+b

Here c denotes consumption, u(c) the instantaneous utility function, the time preference rate, q output and k the depreciation of the capital stock, per unit of time. We assume the function u to be strictly concave. Boom income b 8

is a positive constant over the period [0; T ) and is otherwise equal to zero. In this model the same good can be used for consumption and investment. The technical constraint is de…ned by the following production function: q = g (k) = Ak

+v(')(1

)

; assuming that k = k (kT ; kG ) :

We de…ne k, the state variable of the economy, as a composite good with a physical component (kT ) and an infrastructure component (kG ). The latter is thought of as a pure public good as de…ned by Samuelson (1954). In the model, instabilities are indirectly considered through the elasticity applied to capital, ', which depends upon public externalities. With reference to our …rst assumption, we do consider that this elasticity acts on the economy in a non-linear manner : v (') : v (0) = 0; v (') = 1, lim v (') = d, with d > 1: '!1

These conditions stress the main role played by infrastructure capital for private production and the existence of a limit to increasing returns in capital. They imply speci…c properties on the structure of the economy: 8 < = Ak for 0 < ' < ' = Ak for ' = ' g(k) : = Ak +v(')(1 ) for ' < ' d

Contrary to Murphy, Shleifer & Vishny [1989], Azariadis & Drazen [1990], d’Autume & Michel [1993] & Vellutini [2003], threshold e¤ects ar not related to the level of capital stock, but to public externalities. With reference to Krugman [1991] and Matsuyama [1990], the presence of thresholds point out the critical role expectations can play in de…ning the long run performance of an economy. Moreover, this approach allows us to consider both endogenous and exogenous growth situations in the same analytical framework, assuming that the multiplicity of these situations might reveal a structural instability concerning the dynamical regimes in which the economy evolves: when 0 < ' < ', returns are globally decreasing with respect to any accumulable factors of production. The reduced form aggregate production function has the standard neoclassical properties. The economy is hence in the Solow regime. We …nd here the model of Collier & Gunning [1995].Only one feasible path is compatible with this dynamical regime. When ' ' d, returns can globally increase (or remain constant) with respect to accumulable factors of production. Consequently, the dynamic regime is generated by the complementarity between private and public capital. We de…ne the latter as the endogenous growth regime. A multiplicity of feasible paths are compatible with this dynamical regime. Note that for a speci…c value of the complementarity coe¢ cient, the reduced form aggregate production function becomes linear in capital. In this case, we shall say that the economy follows a speci…c path, the Romer path. 9

3.1

Instabilities and multiple equilibria

An accurate analysis of the dynamical properties of the model is now necessary in order to isolate situations where the economy faces a kind of structural instability. The problem at time t = 0 is to choose an optimal consumption path taking into account that the boom will be over at time T . The solution for the latter is well-known and follows: 8 < k=q k c+b 0 g(k) : c = u00(c) ( + ) , with = + v (') (1 ) u (c)

u0 (c) u00 (c)

where

k

is the intertemporal elasticity of substitution. Initially the

economy is in steady state equilibrium with the capital stock equal to k. We study the local dynamics of the feasible paths using the characteristic roots of the linearisation of this (non-linear) di¤erential-equation system. We …rst form the Jacobian matrix and evaluate it at the steady state point k; c : JE =

"

@k @k @c @k

@k @c @c @c

#

(k;c)

The four partial derivatives, when evaluated at the steady state, E, turn out to be: g (k) @k = @k k E

@k @c

=

1

=

u0 (c) u00 (c)

E @c @k @c @k

E E

=

[u

00

g 0 (k) g (k) k 2

000

2

(c)] +u (c)u0 (c) [u00 (c)]2

g (k)

( + ) = 0:

k

It follows that the Jacobian matrix takes the following form: 3 2 g (k) 1 k 5 JE = 4 0 u0 (c) g (k) g (k) 0 2 00 u (c) k (k;c) The qualitative information we need to assess the dynamical properties around the steady state can be extracted from the following equation, P (x) = 0 u0 (c) g (k) g (k) x2 T x + D, with T = g(k) and D = . Our analysis 2 00 (c) u k k identi…es two stylised dynamical regimes: the Solow regime and the endogenous growth regime. The …rst one describes a world without any memory. The second one describes a world subject to history or/and expectations. We illustrate their speci…c stability properties by using the graphical tool of potential functions commonly used in physics, which consists of describing a steady state as the minimum of a curve of potential. This curve is drawn by the solutions of a 10

dynamical system5 . The advantage of the potential function in explaining the rules governing the evolution of the economy lies in the fact that it makes the dynamics of an economy inside as well as outside its steady state explicit. The behaviour (or arbitrage) of the individuals trying to maximise pro…ts and utility can push the economy to the minimum of its potential curve. If the slope of the potential curve is steep for some volume of capital stock, it indicates that the steady state is stable. By contrast, in situations where the slope is relatively small, the adaptative dynamics will probably change the economy rather slugishly in the direction of the initial steady state and there is some likelihood of observing the stock of capital in such con…gurations outside the equilibrium. 3.1.1

The Solow regime

Proposition 1 When 0 < ' < ' or 0 < < 1, the steady state is a neoclassical stationary path. For any initial condition, the economy is trapped in the Solow regime. Once trapped, the economy grows on private capital accumulation, and growth might eventually peter out without any exogenous sources. The positive trade shock does not have signi…cant impact on the long run path of the economy. The transition path does not modify the properties of the steady state. Proof. If D < 0 and T > 0 or g(k) k > , the two eigen values are real with opposite signs. the dynamical system has a unique steady state which is saddlepath stable. We observe such a situation when capital is subject to diminishing g 0 (k) g (k) returns, < 0. 2 k

Insert Figure 7 In the Solow regime, any response to a temporary positive trade shock involves two phases. During the …rst one, the capital stock increases as part of the boom income is invested. During the second phase, a barrier of potential emerges between the two equilibria (the one before the shock, the one after the shock) as investment is reversed enabling a higher consumption level. Investment smoothes consumption, the latter jumping up at time t = 0 and then declining monotonically towards its pre-shock level. In this case, neither history nor expectations can in‡uence the long-run feasible path of the economy. The dynamical regime mainly results from technical constraints imposed to capital and resumed in the so-called Inada conditions. Any positive trade shock will modify only temporarily the motion of the main aggregates, without however preventing their convergence towards the initial equilibrium. In this ergodic world, the notion of instability expresses here only a temporary irregularity in the dynamics of the state variable. In other words, the economy cannot be affected by this irregularity, its dynamical properties deeply rest on an invariance condition. 5 A dynamic system with negative roots engenders a shaft with an incurved bottom, re‡ecting the existence of a unique steady state. Moreover, a dynamic system having one of the roots being nil, produces a shaft with a ‡at bottom, re‡ecting a multiplicity of equilibria.

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3.1.2

The endogenous growth regime

Proposition 2 When ' ' d or 1, and [g 0 (k) g (k)] =k 2 0 the steady state is fundamentally unstable. The economy faces structural instability with reference to the muliplicity of paths it can follow. Because of this structural instability, a temporary positive trade shock can induce a durable change in both the dynamical paths and states of the economy. More particularly, the adjustment path, by the reversibility of investment, can lead to expectational undeterminacy. Three di¤ erent con…gurations are now possible: the Romer path, the con…ned path, the limit-cycle. The Romer path Proof. when D = 0 and T > 0, one eigen value is real and positive, while the other is nil. In this case, the system is unstable. The = A and = 1, Romer path is characterised by particular conditions: g(k) k which implies that A > . Along this path capital is subject to constant returns [g 0 (k) g (k)] =k 2 = 0: In this case, the potential curve is ‡at. Only history matters in this economy and any shock is totally consumed. This path is mainly based on a critical amount of domestic capital which allows spillovers impacts to be under "control". We do consider that this path is not really attainable for the kind of economies we deal with in the present paper. We refer here to our assumption that spillovers e¤ects vary according to the development stage. 2

The con…ned path Proof. When D > 0, T > 0 and D > T4 , the two eigen values are complex with negative real parts. The economy converges to the steady state in an oscillating manner. We note that the trade shock does not initiate the transition from one equilibrium to the other, it is rather a structural change resulting from the adjustment process which distorts the form of the curve of potential. In this respect, the oscillation of the state variable makes the possible ex-ante equilibria disappear, leaving only one ponctual attractor assimilated as a poverty trap. The limit-cycle Proof. When T = 0 and D > 0, the eigen values are complex with 0 real parts. Then the trajectories are ellipses around the steady state. This system neither converges nor diverges. The type of equilibrium is called a limit-cycle. In this case, the adjustment process leads to the formation of a periodic attractor. In response to a trade shock, the transition paths oscillate around the steady state. The economy faces greater volatility in its main aggregates without revealing any long run growth perspective. This particular dynamical property is another expression of what we can call a poverty trap. Insert Figure 8 In these last two cases, only expectations matter. For given initial conditions, the equilibrium condition may not uniquely pin down the initial value. There 12

may be multiple equilibrium paths, with self-ful…lling expectations. The postshock steady state is no longer neutral with respect to the pre-shock steady state (the Solow regime). Moreover, it is no longer dependent upon this pre-shock steady state (the Romer path). The post-shock steady state is now de…ned by the path which has been taken (the con…ned path or limit-cycle). It is mainly individual expectations, whether pessimistic or optimistic, which determine what the impact of a positive shock would be on the economy. In this respect, it is important to note that the shock-response dynamics is distorted when the structural parameters move away from their reference value6 . In other words, instabilities can irreversibly modify the structure of the economy, in parallel with the sole motion of the state variable. Consequently, two systems starting with the same initial conditions can end up in two di¤erent equilibria. In these situations where nonconvexities and feedbacks are important, forces re‡ecting individual expectational behaviours can generate an equilibrium constellation in which they play a decisive role in determining the future evolution of the economy, namely the unstable steady state. In the absence of these forces, the equilibrium k; c would not change. But an in‡uence acting in the economic situation described by the potential function - or a ‡uctuation, in the terminology of dynamic systems theory - will necessarily move the economy to a multiplicity of equilibria.

3.2

Structural change, path-dependence and shock-response strategies

In the Solow regime, it is rather the ex-ante nature of the shock which allows the transition from one attraction basin to the other. By contrast, on the Romer path, any shock leads the system to a new equilibrium. We observe, however, that in both cases, the structure of the global dynamics, that is to say the form of the curve of potential, is not a¤ected by the shock. Consequently, shocks make the equilibrium to move along a curve or a ‡at line, place of feasible growth paths, without modifying the con‡ict between the di¤erent attractors. However, When > 1 a temporary positive shock can generate a structural shift in terms of a notable change in the growth potential of the economy, (in the form of the potential curve). Some authors showed that shock e¤ects can lead to this remanence property of dynamical systems (Amable & al., [1992]). This property suggests that a control parameter subject to a …rst variation, then another one of identical amplitude and opposite way, leads the system to another steady state. We consider that this property is interesting when we address attention to shoch-response strategies applied in Sub-Saharan countries which are prone to trade shocks. Analytically, we admit that generally dynamical systems under hysteresis questions the multiplicity of potential equilibria and the associated undeterminacy. In dynamic systems theory, a structurally shifting shape of the potential curve is called a phase transition and it occurs if the parame6 This speci…c property leads to extend the concept of punctuated steady state to equilibrium dynamics, substituting the notion of equilibrium for the one of attractor.

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ters describing the relevant in‡uences and forces acting upon the system under concern pass across some critical borders. A special case is shown in Figure 4, where the transition drawing, …rst from the left to the right (shock), second from the right to the lelft (post-shock), can be called a bifurcation. The economy, which …rst is located in its initial steady state, is later to be found far from the latter. In this situation there are di¤erent directions open for the further economic evolution, and without any detailed knowledge about the ‡uctuations resulting from individually expectations behaviour, the further direction of the economy cannot be predicted ex ante. In this respect, the issue of the multiplicity of equilibria is important when one of the roots of a dynamical system is nil. This is the case in the endogenous growth regime. The corresponding solutions consist of locating one stationary equilibrium whose stability would express a loss of memory with reference to initial conditions, and a non stationary one whose instability would result in a strong submission with historical data. However, the latter also depends upon adjustment parameters that trace the curve of the transition paths. In a deterministic framework, we must concede that these paths are fundamentally linked to a given initial point. Consequently, the path dependence of the equilibrium is only a joint product of the sole property of dependency on initial conditions. Nevertheless, in an uncertain framework, any dynamical system would evolve according to the series of random shocks to which it is submitted. Thus, the property of path dependence not only concerns transition paths, but also the chronic of shocks. In this last case, it does not seem improper to evoke such a property. Finally, we retain that the previously quoted divergence results in the way we conceive the shock. If the invariance of the system’s dynamical structure must be preserved, the nature of the shock would have to be such that the gap between the current state and the deterministic-equivalent equilibrium one remains statistically stationary. If it is not the case, we would talk of structural instability. The impact of instabilities on the adjustment process can easily be stressed using the following logarithm proxy of the adjustment equation: hf

g

u ln A + k:

Thus, instabilities are taken into account by observing the adjustmentssequence fhgthrough the one of the capital fkg. This analysis leads us to study the path-solution fpgaccording to its proper variance, the one that should reveal R 2 an additional instability in the model. Suppose that V h u f (k Ek) p (k) dk exists, then we can deduce the following de…nition V h u V k. Knowing that and k are independent and the mean value of returns to capital remain constant, we conclude that E 2 k 2 = 2 k 2 with 2 = E 2 . Consequently, for given initial conditions, the growth potential of the economy might lead to a growing instability of the adjustment path : V h u v 2 V k . This last expression points out that the variability of the adjustment path is strictly proportional to the one of the capital stock. However, the variance of the capital stock positively depends upon the variability of the corresponding returns. 14

Moreover, adjustment to a temporary positive shock might be subject to individual strategic behaviours. The resulting transition path can then be the result of individual activities that create an impulse strong enough to force the economy irreversibly into the convergence basin of one of the multiple equilibria. To illustrate that point, consider a developing country which has an imperfect access to the world capital market: the latter can hold foreign assets, k ;but it cannot borrow (k k ). At time t = 0 the world interest rate is lower than the time preference rate ( > r ). Before the shock, the domestic rate of return exceeds the world rate of interest: there is an incentive to borrow. In this open capital account model, the shock-response strategy depends upon two activities: investing abroad or investing in the domestic economy. Initially windfall savings are invested domestically until k is reached. For the remainder of the boom period investment is in foreign assets. These two activities are linked, because the individuals can substitute their e¤orts across the two. In this country, the presence of nonconvexities combined with a wealth-dependent borrowing constraint, can imply a competition between these activities. Formally, an individual chooses k = (k; k ) to maximise the payo¤: V (k). The best response of each individual can be given by the following …rst-order condition: @Vf g = r(k) @k

2

(k

k ) , with 0

1

The second term of this …rst order condition represents the marginal cost of investing in the country, where measures the substitutability of the individual’s e¤orts across the two activities. When = 0 the latter chooses the e¤orts in the two activities independently, and their best responses are given by @Vf g @Vf g = r(k ) when k k : Wealth increases @k = r(k) when k < k and by @k in the boom period and then returns to its pre-boom level, foreign assets being rapatriated and domestic investment reversed. By contrast, when 0 < 1 each individual’s e¤orts in the two activities are substitutes. This interdependence makes the individual’s marginal cost of investment in the economy increases with the e¤ort of holding foreign assets. In this case, such an activity is self-reinforcing since it contributes to decreasing the domestic rate of return to capital. Then, foreign assets won’t be rapatriated. This self-reinforcing mechanism, which rests on agglomeration economies, is an illustration of the path-dependence property and can explain why the economy can be trapped on the con…ned path or a limit cycle; two representations of the so-called poverty trap. To illustrate this last point, consider that Vf g can be de…ned on the set D = 0; k . Then, D0 := ( 1; 0] [ [B; 1) and Vf g (k; k ) = 0 for all k 2 D0 . If < 1, the relation has a maximum level on the set 0; k and all distributions of the capital stock should remain in the following zone of the phase diagramme ) V k ; k . However, we note that Vf0 g (k) = g(k) 6= g(k for all 1. If hk h k > 1 we de…ne the sets D1 := [0; k [ and D2 := k ; e k , then there exists two points k 2 D1 and e k

k

2 D2 ; such that V (E) := [1; 15

]

D1 [ D2

h i for E := k ; e k k . As a result, any transition path penetrating the region E from the phase diagramme will be orientated to one of the previously de…ned sets D1 and D2 , or oscillate between the latter. In both cases, the adjustment path is fundamentally non deterministic with regards to its arrival point, considering the presence of this switching regime zone results from the unstable nature of the returns to capital.

4

Conclusion

The validity of the poverty trap view on SSA countries su¤ers from the low instability – low growth relation imbedded in it. As analysed in the …rst part of this communication, several empirical evidences support an inverted relation. Featuring complementarity e¤ects an optimal growth model - presented in Section 3 - emphasizes that even a temporary positive shocks can lead to poverty traps equilibrium. Thus instability matters for long term growth. Policy implications are far reaching. Management of shocks is no longer a question of the short run. Stabilisation mechanisms as well as compensatory payments play a crucial role for long run equilibrium. In the long run, it becomes crucial to consider the structural features that make low developed countries more prone to shocks. Concerning the allegedly positive relation between openness and growth, it appears that this relation is highly dependent upon the sectoral orientation. Primary exporting countries experiencing structural breaks in their export earnings are trapped. As such, shocks are rather curses than opportunities. Morevoer, shocks (commodity prices, con‡icts, climate,...) experienced by low developed countries are of a "structural break" kind rather than being smoothed ‡uctuations around a well de…ned trend. Poverty traps macroeconomics should take into consideration those speci…c features of SSA countries.

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[6] Basu P. and D. Mc Leod, "Terms of trade ‡uctuations and economic growth in developing economies", Journal of Development Economics, 37, 1992, pp 89-110. [7] Baxter M. and R. G. King, "Measuring Business Cycles: Approximate Band pass …lters for economic time series", The Review of Economics and Statistics 81, 1999. [8] Bevan D.L., P. Collier and J.W. Gunning, "Consequences of a Commodity Boom in a Controlled Economy", World Bank Economic Review, 1, 1987, pp 489-513. [9] Cashin P., H. Liang, C.J. MCDermott, “How persistent are shocks to world commodity prices?, IMF Working Paper, 1999. [10] Collier P. and J.W. Gunning, "Trade Shocks - Consequences and Policy Responses in Developing Countries", International Center for Economic Growth Occasional Papers, 51, 1994. [11] Collier P. and J.W. Gunning, "Trade Shocks: Theory and Experience", mimeo, 55 pp, 1995. [12] Collier P. and J.W. Gunning, "Explaining African Economic Performance", Journal of Economic Literature, 37, 1999, mars. [13] Corden M.W. and J.P. Neary, "Booming Sector and De-industrialization in a Small Open Economy", The Economic Journal, 1982. [14] Cuddington J.T., H. Liang and S. Lu, "Uncertainty, Trade, and Capital Flows in Sub-Saharan Africa", WorkingPapern 6 , Georgetown University, Washington DC, 1995. [15] D’Autume A. and P. Michel, "Hystérésis et piège du sous-développement dans un modèle de croissance endogène", Revue Economique, 2, 1993, pp. 431-50. [16] Day R., Complex Economic Dynamics, Vol. 1, The MIT Press, Cambridge MA, 1994. [17] Deaton A.S., "Commodity prices, stabilization, and growth in Africa", Discussion Paper n 166, Princeton University, 35 pp, 1992. [18] Easterly W.,"Reviving the 50s’: the big push, poverty traps, and takeo¤s in Economic development, Center for Global Development Working Paper, 2005. [19] Easterly W., R. Levine, "It’s Not Factor Accumulation: Stylized Facts and Growth Models," Working Papers Central Bank of Chile 164, Central Bank of Chile, 2002.

17

[20] Easterly, W. , Kremer M., Pritchett L., Summers L. H., "Good policy or good luck?: Country growth performance and temporary shocks," Journal of Monetary Economics, Elsevier, vol. 32(3), pages 459-483, 1993. [21] Géronimi V. and Ph. Hugon, "Instabilité des recettes d’exportation, et changements de trajectoires des économies africaines", dans l’Afrique des Incertitudes, Ph. Hugon, G. Pourcet and S. Quiers-Valette (éds), IEDES Collection tiers Monde PUF, 1995, pp 17-39. [22] Géronimi V., P. Schembri and A. Taranco, "Instabilités et développement : implications pour les politiques de coopération. Une ré‡exion à partir de l’expérience de l’Afrique sub-saharienne sur les trois dernières décennies", dans L’Europe et le Sud à l’aube du XXIème siècle : enjeux et renouvellement de la coopération, EADI – GEMDEV (éds), Karthala (CD-Rom), 2002. [23] Géronimi V., L. Mathieu and A. Taranco, "La nature des ‡uctuations des cours de matières premières: implication des résultats des analyses en séries temporelles pour la stabilisation et le développement économique", in Economie et Sociétés, Série Relations Economiques Internationales, n 37, 2003. [24] Grilli E.M. and M.C. Yang, "Primary Commodity Prices, Manufactured Goods Prices, and the Terms of trade of Developing Countries: What th Long Run Shows", The World Bank Economic Review, 9, n 3, 1988. [25] Guillaumont P. and M. Demeocq, "Export Instability and Development: A summary Review of the Literature", CERDI, 1983, juin. [26] Hnatkovska V., Loayza N., "Volatility and Growth", World Bank Working Paper, 2003 [27] Ho¤ K.,"Beyond Rosenstein-Rodan: The Modern Theory of Coordination Problems in Development", Proceedings of the Annual World Bank Conference on Development Economics 2000,Washington, D.C.: World Bank, 2001, 145-188. [28] IMF and World Bank, Global Monitaring report 2005: Millenium Development Goals: from Consensus to Momentum, Washington DC, 2005. [29] Kose M.A., Prasad S.E. and Terrones M.E., "Financial Integration and Macoeconomic Volatility", IMF Working Paper, 2003. [30] Krugman P., "The Narrow Moving Band, The Dutch Disease, and The Competitive Consequences of Mrs Thatcher", Journal of Development Economics, 27, 1987, pp 41-55. [31] Krugman P., "History versus Expectations", Quarterly Journal of Economics, 106, 1991, pp. 651-67.

18

[32] Love J., "Export Instability and the Domestic Economy: Questions of Causality", The Journal of Development Studies, 28, n 4, 1992, July. [33] Matsuyama K., "Increasing returns, Industrialisation, and indeterminacy of Equilibrium", Quarterly Journal of Economics, 106, pp. 617-50, 1990. [34] Murphy K., A. Shleifer et R. Vishny, Industrialisation and the Big Push, Journal of Political Economy, 97, pp. 1003-24, 1989. [35] Nurske R, Problems of capital formation in underdevelopped countries, Oxford, Basil Blackwell, 1953. [36] Ramey G., V. A. Ramey, "Cross country evidence of the link between volatility and growth", American Economic Review, vol. 85, 1995. [37] Rosenstein-Rodan P.N., "Problems of Industrialization of Eastern and South-eastern Europe", Economic Journal, June-sept. 1943. [38] Sachs, J.D., McArthur J.W., Schmid-Traub G., Kruk M., Bahadur C., Faye M., McCord G., "Ending Africa’s poverty trap", Mimeo, 2004. [39] Scitovsky T., "Two concepts of external economics", The journal of Political Economy, april, 1954. [40] UN Millenium Project, Investing in development: A practical Plan to achieve the Millenium Development Goals, Overview report, U.N., New York, 2005. [41] Vellutini C., Capital mobility and underdevelopment traps, Journal of Development Economics, 71, pp. 435-4, 2003.

19

5

Annexes 1960-2000

1960s

1970s

1980s

1990s

2.80 1.57 0.31

3.75 2.46 1.73

2.75 2.06 1.58

2.09 0.32 -0.034

1.88 1.39 -0.49

Output Volatility (standard deviation) Industrial Countries 2.59 2.18 Developing Countries 4.90 4.62 Sub Saharan Countries 7.42 5.64

2.78 4.83 6.92

2.12 3.89 5.5

1.79 3.39 5.04

Output Volatility (standard deviation of output gap) Industrial Countries 1.27 1.14 2.02 1.18 Developing Countries 2.08 2.13 2.23 1.76 Sub Saharan Countries 4.02 3.13 4.35 3.06

1.05 1.65 3.10

Output Growth Industrial Countries Developing Countries Sub Saharan Countries

Source: Author’s calculations and Kose, Prasad and Terrones [2003]

Table 1: Growth and Volatility Statistics

Box n 1: Delayed coordinates representation An observable time series is the realization of some dynamical process (growth here). To recreate a phase space portrait of the dynamical system under study from a scalar time series, we use delay coordinates To expand a one dimensional time series into an M dimensional phase space, one substitutes each observation in the original time series T(t) (the growth rate) with vector : Y(i) = (T(i), T(i+d), T(i+2d),. . . , T(i+(m-1)d), where i is the index time, m is the embedding dimension and d the delay time. As a result, we have a series of vectors: Y={Y(1),Y(2),. . . ,Y(N-(m-1)d)} where N is the length of the original time series. Mutual information can be used to determine optimal value of the time delay d. False nearest neighbours method can be used for choosing the minimum embedding dimension m.

20

8 SSA industrial countries

6

developing countries

5 4 3 2 1 0 1960

1970

1980

1990

2000

Figure 1: Moving volatility: 5 years window 1960-2000

8

Output growth

Standard deviation

7

6 4 2 0 -2 -4

0

5

10

15

volatility Figure 2: Growth vs Volatility in SSA (1960-2000)

21

20

Confidence ellipses in delayed GDP per capita g rowth rates (1961 - 2000)

15 Burkina Faso

10 Guinea

5 Kenya France USA

0

Growth rate at t

Benin

-5 Mali

-10 Ethiopia Niger

-15

-15

-10

-5

0

5

10

15

Growth rate at t-1

Figure 3: Con…dence ellipses in delayed GDP per capita growth rates

Countries/products Alumina Crude petroleum

Copper Cotton Co¤ ee

>50% earnings Guinea Angola, Gabon, Rep. Congo, Nigeria Zambia

[20%,49%] earnings

Cameroon, Guinea

5 years 82-86 DS 116 months>5 years 64-74-82-93 TS (LSTAR) 2 months5 years 65-75-81-86-93 DS 1 >5 years 75-88-93 TS (LSTAR) 10.5 months5 years 62-73-86 DS 29 months5 ans 63-75-80 TS (LSTAR) 1 >5 years 61-74-86

Source: Author’s calculation and Cashin et al.[1999]

Table 3: Unit root tests and persistance measures

23

Distance dispersion scatterplot (GDP per capita growth rate, 1961 - 2000) 30 28

SSA countries Others countries

26 24 22 20 18 16 14 12 DISPERSION

10 8 6 4 2 0 -2

0

2

4

6

DISTANCE

Figure 5: Distance dispersion scatterplot

24

8

10

12

Distance dispersion scatterplot (GDP per capita growth rate, 1961 - 2000) 30 28 Instability and Stagnation Instability Stability and Growth

26 24 22 20 18 16 14 12 DISPERSION

10 8 6 4 2 0 -2

0

2

4

6

8

DISTANCE

Figure 6: Distance-dispersion scatterplot only SSA countries

25

10

12

k

k*

c Figure 7: The Solow regime

k

k

k

k*

c

c c

Limit Cycle

Confined Path

Figure 8: Endogenous growth

26

Romer Path