Existing quantitative macroeconomic models of developing countries are essentially of two types: the Mundell–Fleming framework, which assumes a complete specialization in production,1 and the “dependent economy” model, which subdivides the production structure into a nontradable sector whose production is consumed locally and a traded sector that produces a single good consumed both at home and abroad. Both models consider a single labor market with a homogeneous labor force and assume that wages either clear the labor market or are partially indexed to prices, thus inducing unemployment. In addition, the tradable-nontradable model assumes that the labor force is perfectly mobile among sectors, which implies that wages equalize across sectors. For reasons of simplicity or data limitations, these models rarely take into account key features of labor and goods markets in many developing countries like Côte d’Ivoire. In particular, these models ignore key dualisms in both labor and goods markets. First, the labor market is not homogeneous but instead fundamentally opposes employees of the formal sector against self–employed and family aides of the informal sector. Second, the tradable sector is not specialized in production and technology, but instead groups together modern highly productive industries on the one hand, and agricultural activities of small farm units producing traditional exportable goods with low productivity, on the other hand. To the extent that these dualisms are central to the adjustment of developing economies, they may seriously challenge the simulation properties of both the Mundell–Fleming and the “dependent economy” models.

Abstract

Existing quantitative macroeconomic models of developing countries are essentially of two types: the Mundell–Fleming framework, which assumes a complete specialization in production,1 and the “dependent economy” model, which subdivides the production structure into a nontradable sector whose production is consumed locally and a traded sector that produces a single good consumed both at home and abroad. Both models consider a single labor market with a homogeneous labor force and assume that wages either clear the labor market or are partially indexed to prices, thus inducing unemployment. In addition, the tradable-nontradable model assumes that the labor force is perfectly mobile among sectors, which implies that wages equalize across sectors. For reasons of simplicity or data limitations, these models rarely take into account key features of labor and goods markets in many developing countries like Côte d’Ivoire. In particular, these models ignore key dualisms in both labor and goods markets. First, the labor market is not homogeneous but instead fundamentally opposes employees of the formal sector against self–employed and family aides of the informal sector. Second, the tradable sector is not specialized in production and technology, but instead groups together modern highly productive industries on the one hand, and agricultural activities of small farm units producing traditional exportable goods with low productivity, on the other hand. To the extent that these dualisms are central to the adjustment of developing economies, they may seriously challenge the simulation properties of both the Mundell–Fleming and the “dependent economy” models.

Existing quantitative macroeconomic models of developing countries are essentially of two types: the Mundell–Fleming framework, which assumes a complete specialization in production,1 and the “dependent economy” model, which subdivides the production structure into a nontradable sector whose production is consumed locally and a traded sector that produces a single good consumed both at home and abroad. Both models consider a single labor market with a homogeneous labor force and assume that wages either clear the labor market or are partially indexed to prices, thus inducing unemployment. In addition, the tradable-nontradable model assumes that the labor force is perfectly mobile among sectors, which implies that wages equalize across sectors. For reasons of simplicity or data limitations, these models rarely take into account key features of labor and goods markets in many developing countries like Côte d’Ivoire. In particular, these models ignore key dualisms in both labor and goods markets. First, the labor market is not homogeneous but instead fundamentally opposes employees of the formal sector against self–employed and family aides of the informal sector. Second, the tradable sector is not specialized in production and technology, but instead groups together modern highly productive industries on the one hand, and agricultural activities of small farm units producing traditional exportable goods with low productivity, on the other hand. To the extent that these dualisms are central to the adjustment of developing economies, they may seriously challenge the simulation properties of both the Mundell–Fleming and the “dependent economy” models.

The approach followed here postulates that dualism affecting employment, production, and wage determination in many developing countries can be captured by considering that the economy is divided into three sectors: the rural sector, the urban formal sector, and the urban informal sector. The rural sector is composed to a large extent of self–employed persons and unpaid family members. Capital is scarce whereas labor is abundant, which implies that the sector features low levels of labor productivity and incomes. The formal urban sector consists essentially of medium– and large–scale enterprises producing mainly industrial goods using skilled and unskilled labor. Workers are hired through formal contracts, wage settlements are subject to labor regulations, and wages are negotiated through collective bargaining mechanisms. Public employment is considerable and wage increases initiated in the public sector are largely transmitted to the private sector, especially in sub–Saharan African countries. By contrast, the informal sector consists essentially of self–employed individuals and small, family–based enterprises. There are no labor regulations and trade unions. Remunerations are highly flexible and are affected by overall labor market conditions, in particular labor migrations from the rural sector and the formal urban sector.

The purpose of this paper, primarily inspired by the case of Côte d’Ivoire, is to develop and analyze a quantitative macroeconomic model that accounts for these sectoral breakdowns of both goods and labor markets in the modeling of developing countries. The primary concern of our analysis is to examine the implications of this alternative modeling for the dynamic adjustment of employment, production, and other key macroeconomic variables to standard macroeconomic shocks.

Table 1.

Côte d’Ivoire: Population and Employment, 1980-92

(As a percentage of labor force)

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Source: Bodart and Le Dem (1995).

I. The Labor Market in Côte d’Ivoire2

Table 1 presents some basic data on the population and labor force in Côte d’Ivoire over the period 1980–92. We assume that open unemployment is nonexistent, although official estimates of unemployment are published by the Ivoirien authorities. Given the lack of unemployment benefits, it is likely, however, that most of these reportedly unemployed workers have some minor activity in the informal sector. For that reason, these people are reported in Table 1 as workers in the informal urban sector, although it is likely that this sector comprises massive underemployment.

It appears from Table 1 that a substantial share of the labor force is employed in the agricultural and the informal urban sectors, while the share employed in the modern urban sector remains very limited. For example, our estimates indicate that in 1992, only 6 percent of the labor force was employed in the modern urban sector, both private and public. The data reported in Table 1 also indicate that between 1980 and 1992, the lvoirien economy underwent major shifts in the sectoral allocation of labor. The 55 percent increase in the labor force over the period was absorbed by the urban informal sector to a large extent and the agricultural sector to a lesser extent, while employment in the modern sector steadily decreased over time. It follows that, in proportion to the total labor force, employment in the agricultural sector and the modern urban sector declined, whereas the size of the informal sector substantially increased. Over the period considered, the growth rate of the urban population almost doubled, a growth rate at least three times higher than the growth rate of the rural population. This large rural–urban gap in population growth suggests that the strong increase in urban population is due to a large extent to massive rural–urban migration flows. As access to the modern urban sector is rather limited, it is likely that most of these migrants ended up in the informal urban sector.

Over the period 1987–91, the overall economic activity in Côte d’ Ivoire grew by only 3 percent, mainly driven by a strong deterioration in the world prices of the main commodities exported by the country (cocoa, coffee, and cotton). Undoubtedly, this growth rate was insufficient to keep up with the strong growth of the labor force, which vrew by more than 5 percent over that period. Sectoral data show that over the same period, agricultural production grew by about 20 percent, thereby largely exceeding the growth rate of agricultural employment. This suggests that the agricultural sector experienced a considerable improvement in labor productivity. Conversely, in the informal sector, the sizable increase in the labor force has not been accompanied by a similar increase in production. This result supports the presumption that a large part of the labor force in that sector was underemployed in 1991, or, in other words, that there was a substantial potential for labor productivity gains.

Rough estimates of remuneration in each sector of activity are reported in Table 2. These estimates first suggest that there exists a sizable and rather stable spread between the agricultural areas and the urban areas. It is likely that this income differential motivated many rural workers to migrate toward cities, even if the probability of securing a highly paid job in the urban sector was rather small.3 These estimates also suggest that within the urban sector, the average wage rate paid to workers in the formal private sector is about four times higher than the average income received by informal workers. This formal–informal wage differential can be related not only to the significant differences in the productivity and skills between the two classes of workers, as measured by the average nominal value added per worker, but also to the influence of trade unions and formal wage– setting procedures. Finally, by contrast with the other sectors, the observed decline in the overall activity translated into a continuous decline of wages in the informal sector over the period 1987–91. The analysis developed in the following sections presents a formal assessment of these sectoral developments, in particular, it investigates how and to what extent the sectoral allocation of labor is affected by external disturbances and policy responses of the type encountered by most developing countries.

Table 2.

Côte d’lvoire: Sectoral Remunerations, 1987-91a

(In thousands of CFAF, at current prices)

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Source: Bodart and Le Dem (1995).

Remuneration in the agricultural and urban informal sectors is measured by the nominal average product per capita.

II. The Model

This section describes a dynamic model of a small, open developing country with a pegged exchange rate regime and perfect capital mobility. The economy is composed of three sectors of production: the agricultural sector, the urban formal sector, and the urban informal sector. The agricultural sector produces two types of goods, one that is exported and one that is not. In what follows, the first type of goods is referred to as agricultural exports while the second type of goods is referred to as agricultural food crops. Production in the urban formal sector consists essentially of manufactured goods, which are sold in both the international and domestic markets. Conversely, the output of the urban informal sector consists only of nontraded goods, that is, domestic services, handicrafts, or petty trade. As domestic services account for a large part of the output in the informal sector, the production of this sector will be referred to as nontraded services. The imports of the country comprise only manufactured goods, which are imperfect substitutes for the goods produced by the modern urban sector.4

The total labor force is allocated among five activities: the production of agricultural food crops, the production of agricultural exports, the production of manufactured goods, the production of nontraded services, and the production of public goods. Workers in the agricultural sector are assumed to consist only of self–employed persons and nonpaid family aides whose income is equal to the average agricultural product. They are assumed to allocate their time between the two agricultural activities according to the profitability of each activity. In the urban modern sector, wages are indexed to public wages, whereas the amount of labor employed is determined according to the profit maximizing behavior of producers. Public employment and wages are both set exogenously. Finally, labor in the informal sector consists of all of those workers who failed to secure a job in the urban formal sector. Informal workers are all considered to be self–employed persons. Their “wage” rate is equal to the average product and is therefore perfectly flexible. The model also allows for rural–urban migrations. It is assumed that the decision to migrate depends on the wage differential between the rural sector and the urban private sector.

On the demand side, the model assumes that households allocate their disposable income between agricultural food crops, manufactured goods, whether imported or produced domestically, and the nontraded services provided by the informal sector. The model includes public and private investment. Private investment takes place only in the urban modern sector. Investment goods are assumed to consist only of manufactured goods, whether imported or produced domestically.

Finally, the model assumes Walrasian equilibrium in every domestic commodity market. The economy is assumed to be a price taker in the market for its exports of agricultural and manufactured goods and the market for its imports of manufactured goods.5

Labor, Migrations, and Wage Determination

This section describes how employment and wages are determined in the different sectors of the economy.

The Agricultural Sector

It is assumed that rural households are self–producers who produce two types of goods: agricultural food crops (paddy, maize, cassava, etc.,) and agricultural exports (cocoa, coffee, cotton, etc.,). The production of each good combines two factors of production: labor and intermediate inputs. Labor and intermediate inputs are treated as complementary. For each good, the available technology is then described by a production function relating labor to value added:–6

Vi=Ai[exp(γi*t)]Liβi;γi>0,0<βi<1;i=1,2,(1)

where Vi denotes the value added of sector i at constant prices, Li denotes the labor force employed by sector i, Ai is an efficiency parameter, βi, is the elasticity of output to labor, and the term exp(γi*t) allows for technical progress in sector i.

Open rural unemployment is assumed to be nonexistent, which implies that the sum of workers employed in the two agricultural sectors must equal the initial endowment of rural workers:

L1+L2=Lr(2)

where Lr denotes the rural labor force available at the beginning of the current period.

Rural households allocate labor among, the two productions so as to maximize their revenue, given the price of the two goods and the available technology. Formally, we have

MaxRr=Σi=12PVi*Vi

subject to equations (1) and (2), where PVi is the price index of value added in sector i.

From the first–order conditions for profit maximization, we find that the demand fur labor in each sector is determined according to the following relationship

(β11)logL1=β()+(γ2γ1)t+log(PV2/PV1)+(β21)logL2,(3)

where β()=log(A2/A1).

Linearizing the logarithm of (2), substituting it into (3), and solving the resulting equation under the assumption that β1=β2=β determines the demand for labor in the AF sector:

logL1d=λ0+log(Lr)+μ0*σ(γ2γ1)tμ0*σ*log(PV2/PV1),(4)

where σ=1/(1β)>0,λ0=β0*σ*μ0, and μ0, is the value of L2/Lr for the base year.

Because of adjustment costs, labor is assumed to adjust only partially to its desired level. Assuming a simple adjustment scheme, we ascertain that the actual level of employment in the AF sector is given by

logL1=δ1*logL1d+(1δ1)*logL1(1);δ1>0,(5)

where δ1 is a parameter describing the speed of adjustment, L1(−1) denotes the labor force employed in the AF sector at the beginning of the previous period, and L1d is given by expression (4).

Over time, the quantity of labor available in the rural area is affected by population growth and migration flows between the rural and urban areas. Following the approach of Harris and Todaro (1970), we assume that rural– urban migration is determined by the differential between rural and urban wages.7 To account for the relatively limited employment opportunities in the public sector, only the urban private wage is considered, and thus we have8

Mig=Lr*{Φ0+Φ1*[(Wu/Wr)1]};Φ1>0,(6)

where Mig denotes rural–urban migration flows of the labor force over the current period, Wu is the nominal wage rate in the urban private sector, and Wr is the agricultural wage rate.

The urban private wage rate is defined as

Wu=(W3*L3+W4*L4)/(L3+L4),(7)

where W3 and W4, denote the nominal wage rate in the formal and informal sectors, respectively, and L3 and L4 denote the labor force employed in each sector.

The agricultural wage rate is set equal to the average agricultural product

Wr=Rr/Lr,(8)

which implies that the agricultural wage rate responds to any changes in the average productivity of each sector, the relative price between the two agricultural goods, and the distribution of the rural labor force among the two sectors.

Finally, the rural labor force is determined by

Lr=Lr(1)*(1+λr)Mig(1),(9)

where Lr(−1) is the rural labor force at the beginning of the previous period and λr denotes the biological growth rate of the rural labor force.

The Formal Urban Sector

The formal urban sector produces one manufactured good that is sold both domestically and internationally. Production is obtained by combining three factors: capital (K3), labor (L3), and intermediate inputs (N3). Capital and labor are assumed to be perfect substitutes, while intermediate inputs are treated as complementary to value added. We assume that the technology is described by a CES production function in capital and labor

V3=A3[exp(γ3*t)][θ3*K3ρ3+(1θ3)*L3ρ3]1/ρ3γ3>0,0<θ3<1,ρ3>0,(10)

where A3 is an “efficiency” parameter, θ3 is a distribution parameter related to the share in each factor in total factor costs, and ρ3 is the substitution parameter.

The stock of capital is given in the short term. From profit maximization and after linearization, we can express the demand for labor as follows:

logL3d=χ0+v0*γ3(1σ3*ρ3)tv0*σ3*log(W3/PV3)+logK3,(11)

where χ0 is a constant, σ3=1/(1+ρ3) is the elasticity of substitution between capital and labor, and v0=(1/θ3)*A3(K3/V3)ρ3 evaluated at the base year.

Labor is assumed to adjust partially to its desired level. As before, we assume a simple partial adjustment scheme, and thus we have

logL3=δ3*logL3d+(1δ3)*logL3(1);δ3>0,(12)

where L3d is given by expression (11).

Finally, wages are assumed to be fixed by institutional factors, which, in particular, provide for a full indexation to public wages:

W3=W3(1)*[1+λg],(13)

where λg denotes the growth rate of public wages.

The Informal Urban Sector

The modeling of employment in the informal urban sector is based on the assumption that the informal urban sector absorbs all workers released from the other urban sectors.9 Accordingly, the quantity of labor available in the informal urban sector is given by

L4=LuL3L¯g,(14)

where Lu denotes the urban labor force and is assumed to grow over time at a constant biological growth rate λu:

Lu=Lu(1)*(1+λu)+Mig(1).(15)

For simplicity, we shall assume that λur.

Under the assumption that the capital–labor ratio is very low in the informal sector, the production technology can be described by

V4=A4[exp(γ4*t)]L4β4;γ4>0,0<β4<1.(16)

As already noted, the informal sector consists essentially of self– employed individuals whose revenues can be approximated by the output of their production activities. The nominal “wage” rate of these individuals is therefore expressed as

W4=(PV4*V4)/L4.(17)

According to this formulation, changes in the wage rate reflect changes in the price of informal goods as well as changes in the average productivity of labor.

The Public Sector

The real value added of public administrations is approximated here by their total wage bill at constant prices, namely:

Vg=L¯g*Wg0,(18)

where Lg denotes the exogenously given public employment, Wg, the wage rate paid to civil servants, and the 0 superscript, base–year values.

Public wages are determined according to

Wg=Wg(1)*[1+λg],(19)

where λg is set exogenously.

Output and Demand for Intermediate Inputs

As we assumed that intermediate inputs are complementary to the other factors of production, the production and the demand for intermediate inputs by each private sector are determined according to the following relationships:

Qi=Vi/(1αi);0<αi<1,(20)
Ni=αiQi,(21)

and

i=1,2,3,4,

where αi denotes the base–year share of intermediate inputs in the total production of sector i

The total purchase of intermediate goods by the public administrations is treated as exogenous:

Ng=N¯g.(22)

From equations (21) and (22). the total demand of intermediate goods addressed to each private sector is simply

CIi=Σjαi,j*Nj;i=1,2,3,4;j=1,2,3,4,g,(23)

where αi, j are input–output coefficients. The coefficients are constant.

Aggregate Demand

Real aggregate demand for domestic output is the sum of private consumption, private and public investment, government expenditures, and the trade balance. In this subsection, we discuss how these different components of aggregate demand are determined.

Private Consumption

Private consumption is modeled as a function of the real disposable income and the domestic inflation rate with a partial adjustment mechanism:

logCP=ψ0+ψ1*logCP(1)+ψ2*log(YD/PC)+ψ3*log[PC/PC(1)](24)
ψ1>0,ψ2>0,ψ3<0,

where CP denotes the aggregate private consumption, YD denotes the household disposable income, and PC is the domestic consumer price index. The current inflation rate is introduced so as to account for real cash balance effects.

Private consumption is allocated to three types of goods: agricultural food crops; manufactured goods, whether produced domestically or imported; and services provided by the informal sector. The consumption of each individual good is determined according to

CPi=ci*CPϵci(PCi/PC)ϵi;ϵci>0,ϵi<0;i=1,3,(25)

with the constraint that CP1+CP3+CP4=CP determining CP4. The variables PCi denote the domestic currency price index of each good i, the parameters ϵci denote the elasticities of the consumption of each individual good to aggregate consumption, the parameters ϵi are the respective price elasticities of consumption, and the parameters ci are constants.

Investment

As already mentioned, only private investment in the modern industrial sector is explicitly modeled. Furthermore, we assume for simplicity that investment goods consist only of modern industrial goods, whether domestically produced or imported from abroad. The specification of the private investment function is based on a simple accelerator mechanism. It relates private investment, Ip to changes in output. Under the assumption that the capital stock adjusts slowly to its desired level, we establish that Ip, is determined according to

Ip=κ0+(κ1*κ2)V3κ1(κ2dep)V3(1)κ1>0,κ2>0,dep>0,(26)

where κ0 is a constant, κ1 is the capital–output ratio, κ2 is the adjustment speed of capital to its desired level, and dep is the depreciation rate of capital.

The stock of private capital at the beginning of the current period is given by

K3=K3(1)*(1dep)+Ip(1),(27)

where K3(−1) denotes the stock of capital inherited from the previous period.

Aggregate investment is the sum of public investment and private investment. Assuming that public investment is exogenous, we have

I3=Ig+Ip.(28)
Public consumption

Public consumption is equal to the production of public administrations, which in turn is the sum of the public sector output (Vg) and the government purchases of intermediate goods (Ng):

CG=Vg+Ng.(29)
Trade Balance

Total exports are the sum of agricultural exports and exports of manufactured goods produced in the modern formal sector. Exports of raw agricultural goods are computed as the production of agricultural exports minus the domestic demand for these products, assumed to be limited to intermediate consumption:

X2=Q2CI2,(30)

where CI2 denotes the demand for intermediate goods addressed to sector 2 by the other sectors.

Reflecting profitability motivations of producers, the share of exports in the total production of the modern industrial sector is modeled as a function of the relative prices of manufactured goods in the domestic and international markets. To allow for time lags before changes in relative prices exert their influence on the volume of exports, a partial adjustment scheme is also introduced. Formally, we have

logX3=δx*logX3d+(1δx)*logX3(1);δx>0,(31)
logX3d=x0+logQ3+ϵxlog(E*IP3/P3);ϵx>0,(32)

where x0 is a constant, E is the fixed nominal exchange rate index, and IP3 is the international price index of manufactured goods.

As stressed previously, imports consist only of modern industrial goods, supposedly imperfect substitutes for locally produced goods. Therefore, the share of imports in the domestic absorption of industrial goods is derived as a function of relative prices. Again, to capture dynamic price impacts, the specification of the import function includes a lagged import term. Formally, we have

logM3=δz*logM3d+(1δz)*logM3(1);δz>0,(33)
logM3d=m0+logQD3+ϵm*log(PM/PD3);ϵm<0,(34)

and

QD3=CP3+I3+CI3,(35)

where m0 is a constant, M3 represents the volume of imports, QD3 denotes the domestic absorption of industrial goods, CI3 is the demand for intermediate goods addressed to the modern industrial sector, PD3 is the price index of domestic absorption, and PM is the domestic currency price index of imports.

Commodity Market Equilibrium and Prices

This subsection describes how market equilibrium and output prices are determined.

Our model assumes that the markets for agricultural food crops, locally produced industrial goods, and informal goods are characterized by Walrasian equilibrium, which implies that in each market, output prices adjust automatically and instantaneously so as to clear the market at any time:

Q1=CP1+CI1,(36)
Q3=CP3+I3+CI3+X3M3,(37)

and

Q4=CP4+CI4,(38)

where CIi denotes the total demand for intermediate goods addressed to the sector i. The solution to equations (36), (37), and (38) gives the output prices P1,P3, and P4.

The domestic output price of agricultural exports is related to the exogenously given international price according to

p2=E*IP2/TE(39)

where IP2 is the international price index of agricultural exports and TE is an export tax index.

Similarly, the domestic currency price index of imported goods is given by

PM=E*IPM*TM,(40)

where TM is an import tax index, and IPM the international price for industrial goods.

Other Macroeconomic Identities

The rest of the model consists of a number of sectoral identities and budget balancing equations for the public, private, and external sectors. In particular, the sectors’ financing gaps are computed, and, given ad hoc assumptions for the domestic financing, the model closure determines external financing gaps for each agent, as well as the balance of payments gap. Consistent with the assumption of perfect capital mobility, these external financing gaps are satisfied automatically. Financial stock–flow equations complete the model, including the stock of external debt. Together with the—exogenous—interest rates, stock variables are used in the private and public agents’ current balances as well as in the current account of the balance of payments. However, given the dichotomy introduced in the model, the financial equations do not affect the model’s “real” variables.10

III. Data Construction and Parameter Estimation

The section discusses briefly some of the issues involved in the database construction and provides a short discussion of the parameters imposed on the model.11

Construction of Base–Year Data

For reasons of data availability, 1988 was selected as the base year. Sectoral and aggregate data on production and value added were drawn from Côte d’Ivoire (1993). A main objective was to obtain a reasonable approximation of the model’s sectoral disaggregation from the available classification in 33 sectors. For that purpose, we assumed that the activity of the informal sector was composed of retail trade and services other than banking, insurance, and public services, as well as 50 percent of some industrial activities such as construction, textiles, and agro–industry. With this classification, we find that in 1988 the respective shares of the different sectors in aggregate value added were 18.1 percent for the agricultural food crop sector, 16.0 percent for the agricultural export sector, 30.4 percent for the urban formal private sector, 12.9 percent for the government sector, and 22.7 percent for the urban informal sector. Data on employment in the formal urban sector, the public administrations, and the agricultural sector are drawn from the World Bank (1994) statistical profile on Côte d’Ivoire. The rural labor force is split among the agricultural food crop and export sectors using the information provided by Kanbur (1990) on the distribution of households according to the employment status of the head of household. Employment in the informal urban sector is computed as a residual. Following this methodology, we established the sectoral distribution of the labor force in 1988: agricultural food crop sector, 36 percent; agricultural export sector, 19 percent; formal urban sector. 5 percent: informal urban sector, 37 percent; and public sector, 3 percent.

Aggregate and sectoral data on capital are not available. A rough estimate of the capital stock in the modern private sector was obtained by assuming a capital–output ratio equal to 2. Finally, basic data on the composition of aggregate demand are taken from Côte d’Ivoire (1993), while the balance of payments, public finance, and monetary data are based on IMF staff estimates. Base–year key structural characteristics of the Ivoirien economy are reported in Table 3.

Parameters

The parameters imposed on the model to generate the baseline data and run the simulations are reported in Table 3. Owing to lack of econometric evidence on Côte d’Ivoire, the values of the parameters are either set arbitrarily or drawn from developing country estimates in the literature.

In the agricultural sector, the elasticity of production to labor is set at 0.6, which gives a long–run elasticity of output with respect to relative prices of –0.75.12 The speed at which rural labor is reallocated from one sector to the other is assumed to be slow and is given a value of 0.25 (which corresponds to a mean lag of three years). In the urban informal sector, the elasticity of production to labor is assumed to be low 0.40—owing to the existence of massive underemployment. As far as the modern industrial sector is concerned, the elasticity of substitution between labor and capital is assumed to be 0.8, which is close to most empirical estimates for industrial and developing countries. The distribution parameter q of the CES production function is computed on the basis of base–year data, while the speed at which labor adjusts to its desired level is set equal to 0.40 (reflecting a mean lag of 1.5 years). Finally, the input–output coefficients are drawn from the 1987 Côte d’Ivoire input–output matrix (Côte d’Ivoire (1987)) as transformed to conform to our sectoral classification.

The short–term income elasticity of private consumption is set equal to 0.6. With the adjustment parameter set equal to 0.6, we then obtain a long–run income elasticity of 1.0. The elasticity of consumption with respect to current inflation is assumed to be –0.20, which is consistent with various empirical estimates. The parameters imposed on the individual consumption functions are based on the assumption that agricultural food crops are mainly subsistence goods whose consumption is quite stable and thus less sensitive to changes in aggregate consumption and relative prices than the consumption of goods produced by the urban formal and informal sectors. For the export supply and import demand functions, the long–run elasticities with respect to relative prices are set at 0.8 in absolute value, which is in the range of values reported by several empirical studies.13 The adjustment parameter is set at 0.50 in both functions, thereby providing a mean lag of one year, which is in conformity with the empirical literature. For the investment function, the capital–output ratio is set at 2.00, the speed of adjustment of capital to its desired level is assumed to be 0.25, and the rate at which the stock of capital depreciates over time is given a value of 0.05. Finally, we assign a value of 0.1 to the sensitivity of rural–urban migration flows to rural–urban wage differentials.14

Table 3.

Key Parameter Estimates

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IV. Dynamic Simulations

The main properties of the model are investigated by simulating three standard shocks, adopted here for illustrative purposes. The first shock is an exogenous improvement in Côte d’ Ivoire’s terms of trade, attributable to an increase in its average agricultural export price expressed in domestic currency terms. The two other shocks are policy oriented: a reduction of public wages, and a devaluation of the exchange rate. The dynamic effects of these shocks are examined over a period of four consecutive years, starting in 1988, by comparing the results of the simulations with a baseline scenario.15 The magnitudes of the three shocks are set as a 20 percent permanent change in the absolute level of the corresponding exogenous variables over the four–year simulation period. Reflecting the present functioning of the CFA franc zone, whose exchange rate is anchored to the French franc, we implement the simulations in a fixed rate environment under perfect capital mobility.

Terms of Trade Improvement

The first simulation envisages a 20 percent increase in the international price of export crops (IPX2), fully passed through to producers, while export taxation rates are unchanged.16 The dynamic effects of the shock over the four–year simulation period are reported in Table 4.

During the first year, the producers respond to the induced change in the relative profitability of the two alternative productions by allocating more labor inputs to export crops. This stimulates export crop production by 3 percent, with a corresponding 1.6 percent drop in food crop supply, which pushes food prices up by about 12 percent. Relative price changes lead to a shift in demand toward urban goods, which is accommodated by additional imports and import substitutes. Migration flows to urban areas slow down by about 30,000 persons or about 1 percent of the rural active labor force. As the labor force becomes scarcer in urban areas, value added is reduced accordingly, which pushes the deflator of value added in the informal sector up by about 10 percent. In the urban formal sector, however, the deflator of value added is increased by only 3 percent. After four years, price increases in the food crop and in the urban informal sectors are, respectively, in line with (21 percent) and above (23 percent) that in the export crop sector (20 percent). Urban informal producers are thus the major winners in the medium term, thereby allowing migration flows to revert to the baseline trend while remaining slightly higher in the last period. By contrast, the value-added price of manufactured goods returns to its initial level, as modern firms are rapidly squeezed by, on the one hand, the substantial increase in the price of other sector inputs and, on the other hand, the price-taker position of its exporters.

The private consumption deflator is 6.7 percent higher than in the baseline scenario the first year, and the gap widens to 14.3 percent after four years, although at a slower pace (0.8 percent the fourth year). GDP increases almost disappear after the first two years, and reach only a total of 1 percent for the four-year period, as no permanent increase in the capital accumulation of the formal sector is obtained. This modest result could, however, be improved by using the fiscal margins made available by the induced improvement in government revenue. In response to the improvement in the terms of trade, the external current account balance increases by 3.6 percent of GDP during the first year. This large improvement vanishes over time, though, and is reduced to 3 percent of GDP after four years. This result is attributable to the fact that, as domestic price increases bring the real exchange rate above its initial value, imports continue increasing at a sustained pace while the initial boom in agricultural exports disappears slightly over time.

Table 4.

Increase of 20 Percent in Agricultural Export Prices

(Deviations from baseline scenario, in Percentage change, unless indicated otherwise)

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Deviations in thousands of persons. A minus (-) sign indicates a reduction in the migration flows from the rural sector to the urban sector.

Deviations in percentage points of GDP. A minus (-) sign indicates a deterioration of the balance.

A Decrease in Government Sector Wages

The results of a 20 percent reduction in the nominal wages of civil servants (Wg) are presented in Table 5. The wage reduction is instantaneously and fully passed through to the wage earners of the private formal sector (equation (13)), thus inducing a 8.6 percent increase in labor demand during the first year, owing to improving profitability and decelerating substitution of labor with capital (equation (11)). The additional labor input for the formal sector is taken out of the informal sector (equation (14)), leading to a modest 1.1 percent decrease in employment, on account of the substantial difference in size between the two urban subsectors.

Some indirect effects of the wage cut in the urban formal sector are perceptible in the rural sector. Food crop production suffers slightly from the decrease in demand, which pushes the deflator of value added down by 1 percent during the first year. Consequently, farmers increase the time allocated to export crop production, whose prices are fixed in the world market. Some of these farmers (11,300) decide not to migrate to the cities because of the sharp decline in urban incomes the first year. This initial effect is, however, fully reversed in the following years because, as in the terms of trade shock simulation, workers in the informal sector are those who experience the largest increase in income over the medium term: while their per capita income increases by less than 3 percent in the first year, it increases by about 16 percent after four years.

The GDP deflator drops during the first year by almost 5 percent, leading to an equivalent improvement in Côte d’Ivoire’s external competitiveness. Relative price developments shift demand for goods toward those produced by the formal urban sector (+4.3 percent), and away from food crops (–0.3 percent), goods produced by the informal urban sector (–0.5 percent), and imports (–0.8 percent). In contrast to the strong surge of manufactured exports, agricultural exports decline by an average annual rate of 1 percent over the four years, as an increasing share of agricultural exports is used as intermediate inputs by the manufacturing sector. GDP increases by 1.1 percent and the current account of the balance of payments improves by 0.8 percentage point of GDP. On the demand side, the contraction of aggregate private consumption is modest compared with that of household real income, as the 2.5 percent improvement in real cash balances due to the reduction in the consumption deflator lowers the savings rate (equation (24)). By contrast, there is a boost to private investment, which amplifies the growth effect. Both the external current account and the fiscal balance improve progressively over the simulation period, providing after four years results similar to the terms of trade simulation (respectively, 2.5 percent and 2.4 percent of GDP), but with better growth results.

A Devaluation of the Exchange Rate

The results of the third simulation are presented in Table 6. As the product wage in the formal urban sector decreases, as it did in the wage reduction simulation, output and employment in this sector rise substantially, by 2.8 percent and 5.6 percent, respectively, during the first year. The consequent reduction of the labor supply in the informal urban sector drives up the average income of informal workers as the less productive jobs are eliminated (–0.8 percent). In the agricultural sector, the producer price for export crops increases, as it did in the terms of trade simulation, which induces a shift of rural labor away from the food crop (–2.6 percent the first year) toward the export crop sector (+1.5 percent). Rural–urban migration flows strongly decelerate during the first year (–36,000 active persons) in response to the substantial increase in the relative income of rural households vis–a–vis urban households. Migration flows reverse in the following years, however, with the protracted improvement of labor demand in the formal sector, associated with improved earnings in the urban informal sector, bringing together a steady increase in the per capita urban income. First–year price impacts are about 10 percent for both GDP and private consumption deflators, thereby allowing a 10 percent depreciation of the real exchange rate. However, as prices and incomes in the urban informal sector keep rising, this initial depreciation almost vanishes after four years.

Regarding demand effects, private consumption is more reduced than in the wage simulation, owing to negative real cash balance effects. The real impact on private investment is positive (5.6 percent in the first year), although less than in the wage simulation, thereby contributing to the protracted improvement of GDP, which stabilizes at 2 percent after four years. No J–curve profile is observed for the external current account, as the competitive impacts on import and export volumes are already important during the first year. In the short run, the improvement of the current account amounts to about 1.7 percent of GDP, increasing to 2.2 percent of GDP after four years. The medium–term impact on the external current account is thus smaller than in the domestic adjustment simulation, owing in part to slightly less favorable results for the volume of manufactured exports. As far as the fiscal balance is concerned, medium–term impacts are very similar to those noted in the domestic adjustment strategy.

Table 5.

Decrease of 20 Percent in Public Sector Wages

(Deviations from baseline scenario, in percentage change, unless indicated otherwise)
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Deviations in thousands of persons. A minus (-) sign indicates a reduction in the migration flows from the rural sector to the urban sector.

Deviations in percentage points of GDP. A minus (-) sign indicates a deterioration of the balance.

Table 6.

Exchange Rate Devaluation of 20 Percent

(Deviations from baseline scenario, in percentage change, unless indicated otherwise)
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Deviations in thousands of persons. A minus (–) sign indicates a reduction in the migration flows from the rural sector to the urban sector.

Deviations in percentage points of GDP. A minus (–) sign indicates a deterioration of the balance.

Lessons from the Simulation Exercises and Alternative Specifications

The dynamic response of the economy to each of these shocks is highly sensitive to several important features of the model. At least two equations seem to play a key role in the simulation results: the wage equation of the urban sector, and the production function in the urban informal sector. This subsection reviews briefly the potential impact on the results of alternative specifications for both equations.

Alternative wage–setting mechanisms in the formal urban sector will affect considerably the dynamic time paths of employment, migrations, production, wages, and prices. The present version of the model assumed that wages in the urban formal private sector are fully indexed to government wages, which is not contradicted by the relative stability of both types of wages in the 1980s in Côte d’Ivoire. There is a risk, however, that in a real situation some downward rigidity of nominal wages would be observed in the private sector if the government cuts public wages. With private wages not fully indexed to public wages, the results of a government wage cut would be less favorable than those produced above. With less reduction in the product wage, the private sector supply response would be weaker, allowing for a more modest price decrease in manufactured goods. The formal private sector would absorb fewer workers of the informal urban sector, whose prices would not be stimulated in similar proportions. By contrast, the results of the exchange rate devaluation would not be affected by a modification of the parameter in the private wage equation, as both would remain fixed. Alternatively, if public and private wages are partially indexed to domestic inflation, the results of the devaluation would likely be less favorable.

Each simulation has also clearly shown how the informal urban supply response plays a crucial role in the dynamic adjustment of the economy. As a result of its role of absorbing other sectors’ changes in employment by creating or eliminating low productivity activities, this sector has limited reactions to shocks in terms of output, while experiencing sizable fluctuations in nominal incomes and prices. Output reactions would, however, be amplified if the stock of capital were explicitly introduced in the production function, and if capital accumulation accompanied income fluctuations in this sector. This feature—which we did not consider realistic, given the almost subsistence level of the average income in this sector in Côte d’Ivoire—may be relevant for some developing countries.

V. Conclusions and Policy Implications

Our primary purpose in this paper has been to describe the specifications, parameters, and results of a quantitative macroeconomic model that includes some key features of the labor market in developing countries. While standard approaches consider a single labor market, the alternative approach developed in the present paper divided the labor market into three segments: the urban formal market, the urban informal market, and the rural market. This alternative approach enabled us to account for sectoral differences in wage–setting mechanisms, to integrate migration flows between rural and urban areas, and to investigate how migrations affect economic activity, in general, and the expansion of the informal urban sector in particular.

Although our attention has been devoted to the model itself, rather than to using it to address substantive policy problems, at least two interesting results can be derived from the simulation exercises. The first highlights the economic equivalence of the so–called domestic and external adjustment strategies. The second addresses the need for policies oriented toward the informal urban sector, in particular to limit the domestic price impact following a currency devaluation.

Our simulation exercise showed that a contraction of public wages and a devaluation of the exchange rate have similar positive achievements in terms of macroeconomic adjustment, growth, and fiscal and external balances. This result first suggests that in a small open uncompetitive economy like Côte d’Ivoire, adjustment strategies that target the real wage gap are particularly relevant. It also indicates that in countries with a nominal anchor and without an independent monetary policy, the choice of “domestic” versus “external” adjustment strategies might be less technical than political, and geared to the relative preferences attached to the downward rigidity of nominal wages compared with the exchange rate parity. It must be clear, however, that these conclusions rely heavily on our assumptions regarding wage formation in the urban formal sector. These assumptions are roughly adapted to the Ivoirien case in the late 1980s, but they should be subject to systematic empirical research, with a broader cross–country base, if any generalization of these results is to be made regarding the relative advantages of each strategy.

A second policy implication is the need to accompany adjustment measures with policies aimed at improving the performance of the urban informal sector. Any exogenous increase in the capital at the disposal of producers in the informal urban sector will substantially increase the output supply, as the use of capital goods is very low and substantial catch–up effects in terms of technical progress can be obtained by new equipment.

Policies directed toward the increase of capital in this sector, through public investment or improved access to financing, are thus relevant. Such policies may also, at least partially, offset the price increases that originate in this sector after an exchange rate adjustment.

Undoubtedly, the analysis developed in this paper can be improved in several ways. In particular, it would be useful to assess the empirical relevance of some key specifications, notably concerning the labor market and aggregate demand. In addition, some econometric work to obtain better estimates of some key parameters of the model would be desirable.

APPENDIX Key Additional Identities and List of Variables

Key Additional Identities

Prices

PC1=P1(A1)
PC4=P4(A2)
PC3=PD3*TC(A3)
PI=PD3*TI(A4)
PM=E*IPM*TM(A5)
PD3=[P3*Q3E*IP3*X3+PM*M3]/QD3(A6)
PC=[PC1*CP1+PC3*CP3+PC4*CP4]/CP(A7)
PG=[Wg*L¯g+PNg*N¯g]/CG(A8)
PVi=[Pi*QiPNi*Ni]/Vi;i=1,2,3,4(A9)
PNi=α1,i*P1+α2,i*P2+α3,i*PD3+α4,i*P4;i=1,2,3,4,g(A10)

Gross Domestic Product by Expenditure

Y=(PC1*CP1+PC3*CP3+PC4*CP4)+(PI*I)+(PG*CG)+E*(P2*X2+P3*X3PM*M)(A11)

Household Disposable Income

YD=(PV1*V1)+(PV2*V2)+(PV4*V4)+(W3*L3)+(Wg*Lg)te*(E*IP2*X2)td*(W3*L3+Wg*Lg)+π(A12)

External Current Account

VCA=E*(IPX2*X2+IPX3*X3IPM3*M3irg*IDGirp*IDP)(A13)

Government Overall Balance

VBRG=td*(W3*L3+Wg*Lg)+tp*(PV3*V3W3*L3)+(tc*CP3+ti*I)*PD3+te*(e*IP2*X2)+tm*(E*IPM*M3)PG*CGPI*Igrg*DGE*irg*IDG(A14)

List of Variables

Endogenous Variables

  • CG = real public consumption

  • CIi = real consumption of intermediate good addressed to sector i (i = 1,2,3,4)

  • CP = real aggregate private consumption

  • CPi = real consumption of good i; i = 1,3,4

  • DG, DP = stock of net domestic government, private debt

  • IDG, IDP = stock of net foreign government, private debt

  • Ip = real private investment

  • I = domestic investment

  • K3 - stock of capital in the urban modern sector

  • Li = employment in sector i;i = 1,2,3,4

  • LId = demand for labor in the AF sector

  • L3d = demand for labor in the Um sector

  • Lr = total rural labor force

  • Lu = total urban labor force

  • M3 = real imports of manufactured goods

  • M3d = notional demand of imports

  • Mig = rural-urban migrations

  • Ni = intermediate inputs used in sector i;i = 1,2,3,4

  • P1 = price index of agricultural food crops

  • P2 = domestic currency price index of agricultural exports

  • P3 = price index of domestically produced manufactured goods

  • P4 = price index of nontraded services

  • PC = general consumer price index

  • PC1 = consumer price index of agricultural food crops

  • PC3 = consumer price index of manufactured goods

  • PC4 = consumer price index of nontraded services

  • PD3 = price index of the domestic absorption of manufactured goods

  • PI = investment price index

  • PM = domestic currency price index of imports

  • PG = price index of public consumption

  • PNi = price index of the intermediate consumption of sector i (i = 1, 2, 3, 4, g)

  • PVi = price index of value added in sector i; i = 1, 2, 3, 4

  • Qi = real output of sector i; i = 1,2,3,4

  • QD3 = real domestic absorption of manufactured goods

  • Rr = agricultural revenue

  • Vi = real value added of sector i; i = 1, 2, 3 A g

  • W3 = nominal wage rate in the urban modern sector

  • W4 = nominal wage rate in the urban informal sector

  • Wg = nominal wage rate in the public sector

  • Wu = nominal wage rate in the urban private sector

  • Wr = nominal agricultural wage rate

  • X2 = real agricultural exports

  • X3 = real exports of manufactured goods

  • X3d = notional supply of manufactured exports

  • Y = nominal GDP

  • YD = nominal household disposable income

Exogenous Variables

  • E = nominal exchange rate

  • Ig = real public investment

  • Lg = public employment

  • Ng = real government purchases of intermediate goods

  • IP2 = international price index of agricultural exports

  • IP3 = international price index of manufactured exports

  • IPM = international price index of manufactured imports

  • irg’irp = foreign interest rate on public and private debt

  • rg’rp = domestic interest rate on public and private debt

  • TE = export tax index

  • TM = import tax index

  • TC = index of indirect taxes on consumption

  • TI = index of indirect taxes on investment

  • te = implicit export tax rate

  • tm = implicit import tax rate

  • tc = implicit tax rate on consumption

  • ti = implicit tax rate on investment

  • λr = biological growth rate of rural labor force

  • λu = biological growth rate of urban labor force

  • λg = growth rate of public wages

  • π = exogenous sources of household disposable income

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*

Vincent Bodart is an Economist in the European I Department. He received his doctorate in economics from the University of Namur, Belgium. Jean Le Dem is a Senior Economist in the Policy Development Review Department. He is a graduate of ENSAE, Paris. The authors would like to thank Pierre-Richard Agénor, Pierre Dhonte, and Nadeem Haque for their comments on earlier versions of the paper, and Janet Bungay for editorial assistance.

2

For a detailed analysis of the labor market in Côte d’Ivoire, see Schneider (1992) and Grootaert (1992).

3

The role of the rural–urban wage differential is demonstrated in reverse by the low migration rate—as reflected by similar growth rates of the urban and rural populations—during the 1970s when rural per capita income grew rapidly, thanks to improving terms of trade.

4

In what follows, we will identify each sector with the following index: agricultural food crops (1), agricultural exports (2), urban modern sector (3), urban informal sector (4), and the public sector (g). For simplicity, the following abbreviations are used: agricultural food crop sector (AF), agricultural export sector (AE), urban modern sector (UM\ and urban informal sector (UF).

5

The following notational conventions are used. All variables are expressed in absolute values except when noted. A real variable corresponds to a variable measured at base–year prices. For convenience, time subscripts arc omitted. Unless otherwise indicated, flow variables are defined for the current period, while stock variables are measured at the beginning of the current period.

6

A more general specification of agricultural production would include land and capital as additional arguments of the production function. The simplification done here relies on the assumption that land is essentially fixed and the stock of capital is minimal and the possibilities for its extension are rather limited. Note, however, that the impact on production of changes in and capital can be viewed as implicit in the trend term.

7

The Harris–Todaro (1970) approach does not distinguish between the formal and informal components of the urban sector. For an analysis of rural–urban migrations that introduces this distinction, see Fields (1975) and Cole and Sanders (1985).

8

The specification of the migration function draws on a long tradition of economic studies that explain migrations in terms of sectoral differences in expected wages. For details on that approach, see the seminal work of Harris and Todaro (1970) and its several extensions. It must be noted. however, that several recent studies have investigated alternative approaches. For example, Velenchik (1994) examines the role of cash–seeking behavior in the migration process and provides evidence that migration responds to the composition of rural income, and not just its level.

9

This assumption is rather simplistic and is certainly open to criticism. For example, one can argue that the highly educated workers released from the urban formal sector will accept temporary unemployment rather than take jobs in the informal sector. Evidence supporting this argument is provided by Grootaert (1992). However, it is likely that this unemployment is marginal.

10

A more extensive description of the structural model is provided in Bodart and Le Dem (1995), and a full listing of the model equations is available from the authors upon request. Key additional identities and the complete list of variables are provided in the Appendix.

11

For a detailed discussion of data construction, see Bodart and Le Dem (1995).

12

The long-run elasticity of output to relative prices is derived from equation (4).

13

For a survey of the empirical literature, see Bond (1983 and 1987) and Kouwenaar (1991). For recent estimates for African countries, see Reinhart (1994).

14

Empirical studies investigating the determinants of migration flows use logit models that relate the probability of migrating to several factors, including the average per capita income in the origin and destination areas. These studies use census data and approximate the probability of migrating by the ratio of the number of people born in the origin area and residing in the destination area to the total number of people born in the origin area. A recent study on Côte d’lvoire is Velenchik (1994). Under certain specific conditions, our estimate of the sensitivity of migration to relative wages can be reconciled with the results of this study.

15

This baseline scenario is largely fictional, although based on realistic trends of the exogenous variables.

16

In addition, manufactured export prices UPX3 have been increased by 5 percent to reflect the high content of Ivoirien manufacturing exports in processed agricultural goods (chocolate powder, processed wood, cotton textiles, canned fruits), whose international prices should reflect in part the assumed improvement in the corresponding raw material world prices.

IMF Staff papers: Volume 43 No. 2
Author: International Monetary Fund. Research Dept.