Back Matter
Author: and Mr. Jean Le Dem
• 1 https://isni.org/isni/0000000404811396, International Monetary Fund

### APPENDIX I: List of Equations and Variables

#### I. The Complete Model

1. Labor, migrations, and wages

$\begin{array}{cc}\begin{array}{cc}\left(\begin{array}{c}1-3\end{array}\right)& V\left(i\right)=A\left(i\right)\mathrm{exp}\left[\gamma \left(i\right)t\right]{L\left(i\right)}^{\beta \left(i\right)}\end{array}& ;i=1,2,4\end{array}$
$\begin{array}{cc}\left(4\right)& V3=A3\left[\mathrm{exp}\left(\gamma 3*t\right)\right]{\left[\theta 3*{K3}^{-\rho 3}+\left(1-\theta 3\right)*{L3}^{-\rho 3}\right]}^{-1/\rho 3}\end{array}$
$\begin{array}{cc}\left(5\right)& \overline{V}g=\overline{L}g*W{g}^{o}\end{array}$
$\begin{array}{cc}\left(6\right)& \mathrm{log}L{1}^{d}\end{array}=\lambda 0+\mathrm{log}\left(Lr/2\right)+\sigma /2\left(\gamma 2-\gamma 1\right)t+\sigma /2*\mathrm{log}\left(PV2/PV1\right)$
$\begin{array}{cc}\left(7\right)& \mathrm{log}L1\end{array}=\delta 1*\mathrm{log}{L1}^{d}+\left(1-\delta 1\right)*\mathrm{log}L1\left(-1\right)$
$\begin{array}{cc}\left(8\right)& L2\end{array}=Lr-L1$
$\begin{array}{cc}\left(9\right)& \mathrm{log}{L3}^{d}\end{array}=\chi 0+2*\gamma 3\left(1-\sigma 3\rho 3\right)t-2*\sigma 3*\mathrm{log}\left(W3/PV3\right)+\mathrm{log}K3$
$\begin{array}{cc}\left(10\right)& \mathrm{log}L3\end{array}=\delta 3*\mathrm{log}L{3}^{d}+\left(1-\delta 3\right)*\mathrm{log}L3\left(-1\right)$
$\begin{array}{cc}\left(11\right)& L4\end{array}=Lu-L3-\overline{L}g$
$\begin{array}{cc}\left(12\right)& Lu\end{array}=Lu\left(-1\right)*\left(1+{\lambda }_{u}\right)+Mig\left(-1\right)$
$\begin{array}{cc}\left(13\right)& Mig\end{array}=Lr*\left\{\mathrm{\Phi }0+\mathrm{\Phi }1*\left[\left(Wu-Wr\right)-1\right]\right\}$
$\begin{array}{cc}\left(14\right)& Lr\end{array}=Lr\left(-1\right)*\left(1+{\lambda }_{r}\right)-Mig\left(-1\right)$
$\begin{array}{cc}\left(15\right)& Wu\end{array}=\left(L3*W3+L4*W4\right)/\left(L3+L4\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\right)$
$\begin{array}{cc}\left(16\right)& Wr\end{array}=Rr/Lr$
$\begin{array}{cc}\left(17\right)& Rr\end{array}=PVA1*V1+PVA2*V2$
$\begin{array}{cc}\left(18\right)& W3\end{array}=W3\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(-1\right)*\left[1+{\lambda }_{g}\right]$
$\begin{array}{cc}\left(19\right)& W4\end{array}=\left(PV4*V4\right)/L4$
$\begin{array}{cc}\left(20\right)& Wg\end{array}=Wg\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(-1\right)*\left[1+{\lambda }_{g}\right]$

2. Output determination and demand for intermediate inputs

$\begin{array}{cc}\begin{array}{cc}\left(21-24\right)& Q\left(i\right)=V\left(i\right)/1-\alpha \phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(i\right)\end{array}& ;i=1,2,3,4\end{array}$
$\begin{array}{cc}\begin{array}{cc}\left(25-28\right)& N\left(i\right)=\alpha \left(i\right)Q\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(i\right)\end{array}& ;i=1,2,3,4\end{array}$

3. Intermediate consumption

$\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}\left(29-32\right)& CI\left(i\right)=\underset{j}{\mathrm{\Sigma }}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left[\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\alpha \phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(i,j\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}N\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(j\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\right]\end{array}& ;i=1,2,3,4\end{array}& ;j=1,2,3,4,g\end{array}$

4. Private consumption

$\begin{array}{cc}\left(33\right)& \mathrm{log}CP=\end{array}\psi 0+\psi 1*\mathrm{log}CP\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(-1\right)+\psi 2*\mathrm{log}\left(YD/PC\right)+\psi 3*\mathrm{log}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left[PC/PC\left(-1\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\right]$
$\begin{array}{cc}\begin{array}{cc}\left(34-36\right)& CP\left(i\right)=\end{array}ci*{CP}^{\epsilon ci}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{\left(PCi/PC\right)}^{\epsilon i}& ;i=1,3,4\end{array}$

5. Investment

$\begin{array}{c}\begin{array}{cc}\left(37\right)& Ip=\end{array}\kappa 0+\left(\kappa 1\kappa 2\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}V3-\kappa 1\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(\kappa 2-dep\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}V3\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(-1\right)\end{array}$
$\begin{array}{c}\begin{array}{cc}\left(38\right)& I=\end{array}I\overline{g}+Ip\end{array}$
$\begin{array}{c}\begin{array}{cc}\left(39\right)& Kp=\end{array}Kp\end{array}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(-1\right)*\left(1-Dep\right)+Ip\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(-1\right)$

6. Public consumption

$\begin{array}{c}\begin{array}{cc}\left(40\right)& Cg=\end{array}Vg\end{array}+\overline{N}g$

$\begin{array}{c}\begin{array}{cc}\left(41\right)& X2=\end{array}Q2\end{array}-CI2$
$\begin{array}{c}\begin{array}{cc}\left(42\right)& \mathrm{log}X3=\end{array}\end{array}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\delta x*\mathrm{log}{X3}^{d}+\left(1-\delta x\right)*\mathrm{log}X3\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(-1\right)$
$\begin{array}{c}\begin{array}{cc}\left(43\right)& \mathrm{log}{X3}^{d}=\end{array}\end{array}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}x0+\mathrm{log}Q3+\epsilon x*\mathrm{log}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(\overline{E}*I\overline{P3}/P3\right)$
$\begin{array}{c}\begin{array}{cc}\left(44\right)& \mathrm{log}M3=\end{array}\end{array}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\delta z*\mathrm{log}{M3}^{d}+\left(1-\delta z\right)*\mathrm{log}M3\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(-1\right)$
$\begin{array}{c}\begin{array}{cc}\left(45\right)& \mathrm{log}{M3}^{d}=\end{array}\end{array}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}m0+\mathrm{log}QD3+\epsilon m*\mathrm{log}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(PM/PD3\right)$
$\begin{array}{c}\begin{array}{cc}\left(46\right)& QD3=\end{array}\end{array}C3+I3+CI3$

8. Commodity market equilibrium

$\begin{array}{c}\begin{array}{cc}\left(47\right)& Q1=\end{array}\end{array}CP1+CI1$
$\begin{array}{c}\begin{array}{cc}\left(48\right)& Q3=\end{array}\end{array}CP3+I3+CI3+X3-Z3$
$\begin{array}{c}\begin{array}{cc}\left(49\right)& Q4=\end{array}\end{array}CP4+CI4$

9. Prices

$\begin{array}{c}\begin{array}{cc}\left(50\right)& P2=\end{array}\end{array}\overline{E}*I\overline{P}2/TE$
$\begin{array}{c}\begin{array}{cc}\left(51\right)& PC1=\end{array}\end{array}P1$
$\begin{array}{c}\begin{array}{cc}\left(52\right)& PC4=\end{array}\end{array}P4$
$\begin{array}{c}\begin{array}{cc}\left(53\right)& PC3=\end{array}\end{array}PD*TC$
$\begin{array}{c}\begin{array}{cc}\left(54\right)& PI=\end{array}\end{array}PD*TI$
$\begin{array}{c}\begin{array}{cc}\left(55\right)& PM=\end{array}\end{array}\overline{E}*I\overline{P}M*TM$
$\begin{array}{c}\begin{array}{cc}\left(56\right)& PD3=\end{array}\end{array}\left[P3*Q3+E*IP3*X3-PM*M3\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\right]/QD3$
$\begin{array}{c}\begin{array}{cc}\left(57\right)& PC=\end{array}\end{array}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left[PC1*C1+PC3*C3+PC4*C4\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\right]/CP$
$\begin{array}{cc}\left(58\right)& PG=\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left[{W}_{g}*{\overline{L}}_{g}+P{N}_{g}*{\overline{N}}_{g}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\right]/CG\end{array}$
$\begin{array}{cc}\begin{array}{cc}\left(59-62\right)& PVA\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\left(i\right)=\left[\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}P\left(i\right)Q\left(i\right)-PN\left(i\right)N\left(i\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\right]/V\left(i\right)\end{array}& :i=1,2,3,4\end{array}$
$\begin{array}{cc}\begin{array}{cc}\left(63-67\right)& PN\left(i\right)=\alpha \left(1,i\right)P1+\alpha \left(2,i\right)P2+\alpha \left(3,i\right)\mathrm{PD}\end{array}+\alpha \left(4,i\right)P4& ;i=1,2,3,4,g\end{array}$

10. Gross domestic product by expenditure

$\begin{array}{cc}\left(68\right)& \phantom{\rule[-0.0ex]{1.0em}{0.0ex}}Y=\left(PC1*C1+PC3*C3+PC4*C4\right)+\left(PI*I\right)+\left(PG*CG\right)\\ & +E*\left(P2*X2+P3*X3-PM*M\right)\end{array}$

11. Household disposable income

$\begin{array}{cc}\left(69\right)& YD=\left(PV1*V1\right)+\left(PV2*V2\right)+\left(PV4*V4\right)+\left(W3*L3\right)+\left(Wg*Lg\right)\\ & -te*\left(E*IP2*X2\right)-td*\left(W3*L3+Wg*Lg\right)\phantom{\rule{0ex}{0ex}}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}+\pi \end{array}$

#### II. List of Variables

1. Endogenous variables

CG = real public consumption

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

CP = real aggregate private consumption

CP(i) = real consumption of good i; i=1, 3, 4

Ip = real private investment

I = domestic investment

Kp = stock of capital in the urban modern sector

L(i) = employment in sector i; i=1, 2, 3, 4

L1d = demand for labor in the A-F sector

L3d = demand for labor in the U-M 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

N(i) = 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 non traded 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 non traded 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

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

PV(i) = price index of value added in sector i; i=1, 2, 3, 4

Q(i) = real output of sector i; i=1, 2, 3, 4

QD3 = real domestic absorption of manufactured goods

Rr = agricultural revenue

V(i) = real value added of sector i; i=1, 2, 3, 4, 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

2. 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

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

### APPENDIX II

Table 1.

Côte d’Ivoire: Sectoral Classification Table 2.

Input-Output Matrix A-F = agricultural foodcrops, A-E - agricultural exports, U-M - urban formal sector, U-S - urban informal sector, G - public administration.

### APPENDIX III

BASELINE SCENARIO 1/ The baseline scenario is calibrated on a base-year and generated by the model. The base-year is here referred to as the first-year of the baseline scenario is 1988.

A minus (−) sign indicates that migration flows goes from the urban area to the rural area.

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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. Any remaining errors are solely the responsibility of the authors. The views expressed in this paper do not necessarily reflect those of the International Monetary Fund.

While the “dependent economy” model provides important insights into the adjustment of small developing economies to external and policy shocks empirical economy-wide applications remain extremely rare, however, primarily owing to data limitations. For a recent application, see N. Haque, A. Husain, and P. Montiel (1994).

For a detailed analysis of the labor market in Côte d’Ivoire, see Schneider (1992) and Grootaert (1993).

These estimates report an unemployment rate of 5.5 percent in 1988, of which 4.9 percent consists of first job seekers. This unemployment is essentially located in urban areas, where 10.3 percent of the labor force is reported as unemployed, while the unemployment rate in rural areas is estimated to be only 2.3 percent.

For a description of the data sources and further details on the methodology used to elaborate Tables 1 and 2, see Section IV below.

Workers in the agricultural and urban informal sector are assumed to be self-employed, which implies that their nominal wage is measured by their average product.

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 the rural per capita income grew rapidly, thanks to improving terms of trade.

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 (A-F), agricultural export sector (A-E), urban modern sector (U-M), and urban informal sector (U-F).

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

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 land and capital can be viewed as implicit in the trend term.

We also used the approximation: log(x+y) ≈ log2 + 1/2(logx+logy).

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).

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.

We used the approximation: log(x+y) ≈ log2 + 1/2(logx+logy).

This assumption is rather simplistic and is certainly open to criticism. For example, one can argue that it is likely 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 (1993). However, it is likely that this unemployment is very low.

More complicated specifications of the private investment functions have been attempted without obtaining better simulation properties.

The constant x0 is equal to: log(X3°), where X3° denotes the base-year share of exports in production.

The constant m0 is equal to: log(M3°), where M3° denotes the base-year share of imports in domestic absorption.

For a detailed analysis of the formal and informal urban sectors in Côte d’Ivoire, see Grootaert (1993).

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

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

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’Ivoire 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.

This baseline scenario is largely fictive, although based on realistic trends of the exogenous variables. It is presented in the Appendix III.

For a review of this debate, see, for instance, Lizondo and Montiel (1989).

Although the usual channel through which the Dutch disease increases the real exchange rate is not the level of domestic prices, but the nominal exchange rate.

In addition, manufactured export prices (IPEX3) have been increased by 5 percent to reflect the high content of Ivoirien manufacturing exports in processed agricultural goods (chocolate powder, processed wood, cotton textile, canned fruits), whose international prices should reflect in part the assumed improvement in the corresponding raw material world prices. A simulation of price increases limited to IPEX2 yields less intuitive results where output price for manufactured goods are negatively impacted by the improved terms of trade, as a result of the dismantlement of vertically integrated agro-industries.

These margins, which amount to 1.5 percent of GDP in the first year, could be used, for instance, to implement supply-side policies aimed at increasing the profitability of the formal urban sector, thereby strengthening long-run growth effects.

We are aware that even though a domestic strategy is desirable on economic grounds, its implementation may remain difficult because of political and social obstacles.

It is also worthwhile noting that these large increases in the wages of informal workers have an important effect on the dynamics of migrations. In each simulation presented above, while rural-urban migration flows slow down, they accelerate in the medium term as rural workers respond to wage developments in the urban informal sector.

Labor Market Representation in Quantitative Macroeconomic Models for Developing Countries: An Application to Cote D'Ivoire
Author: Mr. Vincent Bodart and Mr. Jean Le Dem