Income Distribution, Poverty Measures and Trade Shocks:
A Computable General Equilibrium Model
of a Archetype Developing Country
Bernard Decaluwé
André Patry
Luc Savard
Cahier de recherche 9812
Département d’économique
Université Laval
Cahier de recherche 98-14
Centre de Recherche en Économie et Finance Appliquées
CRÉFA
Décembre 1998
DÉPARTEMENT D’ÉCONOMIQUE
Faculté des Sciences Sociales
Abstract
In this paper we use a computable general equilibrium model to study the impact of a trade shock and a tariff reform on household poverty for an archetype developing country. Unlike other studies, we present the income distribution of each household group as a Beta statistical distribution. Also, the income distributions are endogenous in this model. Following a change in the mean income, the income distribution will shift proportionally by the same variation. In contrast of other study, this paper presents the poverty lines as being endogenous. With this specification, the poverty line will change following a variation in relative prices. With the new distributions and poverty line, the poverty levels of the base year are compared with the ex-post values. The Foster, Greer and Thorbecke’s (1984) Pα class measures are
used to quantify the households’ poverty levels. We consider two scenarios. The first is a 30% fall in the world price of the country’s export crop and the second is a reduction of 50% in the country’s import tariffs. For the fall in the world price of the country’s export crop, results indicate a drop in all household incomes and a decrease in the poverty line. A unilateral trade liberalization also has negative consequences on all household incomes. As in the first simulation, the poverty line decreases with a unilateral trade liberalization. The effect of the poverty line is non-negligible in both simulations. In the trade liberalization simulation, the poverty line effect counters the income effect in most cases (Pα. improves). In the other simulation, the poverty line effect attenuates the decrease in the poverty measures.
1 Introduction
In development economics and public policy the distribution of income has been an important concern among the scientific community and the policy makers, moreover a large number of developing economies have implemented or were affected by important macroeconomic changes in the last decade. There is a strong interest in analysing the impact of policy changes and external shocks on the income distribution and poverty in respective countries. Computable General Equilibrium modelling is commonly used to analyse changes of income distribution and poverty in developing economies. Two approaches have been used to undertake this task in a general equilibrium framework. The first is to construct a standard CGE model with desegregated households and compare the changes in income and welfare variables of the representative household of each group. This approach was applied by Benjamin (1996), Rimmer (1995) and Azis (1997) among others. The second approach consists of generating an income distribution function for each socio-economic group allowing for further poverty and distribution analysis. This approach was initially presented by Adelman and Robinson (1979) for Korea and subsequently discussed by Dervis, De Melo and Robinson (1982) and used by Chia et al. and De Janvry, A., E. Sadoulet and A. Fargeix (1991). The second approach clearly offers richer possibilities in terms of analytical tool. For a complete discussion on the approach to analysing income distribution with CGE modelling see Dervis, De Melo and Robinson (1982).
The authors of the second approach use either the lognormal or the Pareto (De Janvry et al. 1991) distribution function to depict income distribution of each household group. The authors do not justify why these functional forms are more appropriate then more flexible forms. In Adelman and Robinson, a statistical test is performed on the lognormal, and in some cases the test (skewness and kurtosis) were not satisfactory. They simply eliminate a socio-economic group (by aggregation) to circumvent the problem. The income distribution modelling approach and the statistical literature provide evidence that other functional forms might be more appropriate to represent income distribution (see Bordley, McDonald and Mantrala (1996)).
We follow these authors by assessing poverty through a general equilibrium model. However, we differ from their approach in two manners. The first is by proposing a more flexible income distribution function. With a more flexible distribution function, problems concerning skewness and kurtosis will less likely appear in our study. The second manner for which we differ from the others is in the way we measure poverty. In our measure, we take into account the endogenous characteristic of the income distribution and the effect of a change in relative prices on the poverty line. This way we will shed some light in the black box pertaining to the behaviour of income distribution and poverty measures following a shock affecting income.
In the following section, we discuss the income distribution used in the paper. Afterwards, we present the measures used to quantify poverty in our analysis. The third section is devoted to the structural presentation of the general equilibrium model used in this study. In the fourth section, we present the social accounting matrix used in this study. The fifth section is left to the interpretations of the results. In the last section of the paper, the conclusion of the study is presented.
2 Income Distribution
In this illustrative case, we aggregated the households into 6 groups representative of those living in an archetype African country. The groups are defined as follow: (i) rural household, (ii) small landowner household, (iii) large landowner household, (iv) urban low-income household, (v) urban high-income household and (vi) capitalist household. To each of these groups we attributed income and demographic characteristics corresponding to developing country. These descriptive data are presented in table 1. As we can observe, the mean income varies from 13.57 for the rural household to 117.72 for the capitalist household. As for the population shares, the small landowner household group has the highest population with 36.1% of the total population. However, the rural household has the highest headcount ratio with 93.3% of its population below the poverty line followed by the urban low-income household with 57.7% of its population below the poverty line.
Table 1: Income and Demographic Characteristics
Rural households Small landowner households Large landowner households Urban low-income households Urban high-income households Capitalist households mean income 13.57 27.75 29.91 23.27 41.49 117.72 maximum income 40.0 50.0 55.0 40.0 60.0 140.0 minimum income 5.0 10.0 15.0 15.0 20.0 25.0 population share 0.13 0.31 0.25 0.17 0.10 0.04 % below the poverty line 93.3% 36.1% 19.4% 57.7% 0.5% 0%
In order to study the question of poverty by household group, we propose an income distribution corresponding to the characteristics of each household group. This distribution will depend on the minimum and maximum income and on the skewness of
the income distribution1. To represent these characteristics into our income distributions,
we use the Beta distribution function (equation (1)). Parameters mx and mn are respectively the maximum and minimum income of a group. As for the parameters p and
q, they influence the shape and the squewness of the distribution.
(1)
(
) (
)
(
)
1 1 1 ) , ( 1 ) , ; ( + − − − − − − = p p q q mn mx y mx mn y q p B q p y I where,(
) (
)
(
mx mn)
y y mx mn y q p B mx mn q p q p d ) , ( 1 1 1∫
+ − − − − − − =Unlike the lognormal, the Beta is much more flexible when it comes to the asymmetric forms it can adopt. Contrary to the lognormal, the Beta can be skewed to the
left or to the right and be symmetric. If p〉 q, the distribution is skewed to left. The mode
1
A left skewed distribution can be illustrated as the mode being inferior to the median. A right skewed distribution is when the mode is superior to the median.
is situated on the left side of the distribution. As the inequality between p and q
increases, the distribution tends to be more left skewed. If q 〉 p, the distribution becomes
skewed to the right. Again, the asymmetry accentuates as the inequality increases. If q =
p, the function becomes symmetric. These three conditions are true only if the value q
and p are larger than unity. 2
In table 2, the parameters assigned to each household are presented. For each case, we have chosen the parameters so that the income distribution concords with the
characteristics of the households groups described in table 1.3 The income distributions
generated from these parameters are presented in figures 1a to 1f.
Table 2: Parameters for the Beta Distribution Function
Rural households Small landowner households Large landowner households Urban low-income households Urban high-income households Capitalist households p 1.3 2.0 3.0 1.8 3.3 6.0 q 4.0 2.5 5.0 3.5 3.0 1.5 mx 40.0 50.0 55.0 40.0 60.0 140.0 mn 5.0 10.0 15.0 15.0 20.0 25.0 poverty line 10 20 30 40 Income 0.01 0.03 0.05 0.07 f(Income) poverty line 10 20 30 40 50 Income 0.02 0.04 f(Income)
Figure 1a : Income distribution rural household Figure 1b : Income distribution small landowner households
2 The Beta can also represent a bi-modal distribution. This is the case when p and q 〈 1. For other possibilities of the value taken by p and q, the interested reader is invited to consult chapter 14 in Johnsons, N. L. and S. Kotz (1970).
3 In an applied study, parameter p and q should be estimated and mx and mn represent the maximum and minimum income of the survey. In our illustrative case, an income survey was generated from the Beta statistical distribution with the parameters specified in table 2.
poverty line 20 30 40 50 Income 0.02 0.04 0.06 f(Income) 10 poverty line 15 20 25 30 35 40 Income 0.02 0.04 0.06 0.08 f(Income) 10 5
Figure 1c : Income distribution large landowner households Figure 1d : Income distribution urban low income households poverty line 20 30 40 50 60 Income 0.01 0.03 0.05 f(Income) 10 poverty line 20 40 60 80 100 120 140 Income 0.01 0.02 0.03 f(Income)
Figure 1e : Income distribution urban high income Figure 1f : Income distribution capitalist households households
These distributions will be use to evaluate the poverty incidence within each group in a general equilibrium framework. Following an external shock on the economy, the distribution will take into account the increase or decrease of the mean income of each household group. As in previous studies, we consider the variance of each distribution exogenous to the model. Thus, the income distribution will shift
proportionally with the change in the mean income.4 We compare the poverty levels of
the ex-post situation with those of the base year with the Foster, Greer and Thorbecke’ Pα
measures. We present these poverty measures in the following section.
3 Poverty Measures
In this paper, we use the Foster, Greer and Thorbecke’s (1984) Pα poverty
measures. With the Pα, we will be able to measure the headcount ratio as well as the
deepness of the poverty within a group. The Pα measure is presented at equation (2).
4 Since we are not aware of how the increase (decrease) of income is distributed (i.e. if the increase (decrease) in the mean income is the result an increase (decrease) in the income of the poorest or an increase (decrease) in the income of the richest), we distribute the gain (loss) to all the household within the group. If the mean income increases by ψ, the income of all the households within a group is raised by ψ. With the above rule, the income distribution will proportionally shift horizontally following a change in income. As stressed by Dervis, De Melo and Robinson (1982), this constraint still remains the biggest challenge in studying income distribution in a general equilibrium context.
(2)
z
I
(
y
p
q
)
dy
y
z
P
z mn,
;
α α∫
−
=
In equation (2), α measures the deepness of poverty and z is the poverty line.
When α = 0, the headcount ratio is derived from equation (2). In this case, the Pα
measures the proportion of the population within a group below the poverty line. With α
= 1, the importance accorded to all individual below the poverty line is proportional to
their income. This measure is named the income poverty gap. As α increases, more
importance is given to the shortfalls of the poorest households in the measure; society
becomes more averse to poverty. In this illustrative study, we set α = 2 to interpret this
last case.
We can summarise the three types of measures derived from the Pα with the help
of figure 2. Figure 2 depicts the Pα measure in relation to income for one individual.
For P0, the relation with income is constant. The measure accords the same weight to the
richest of the poor as it does to the poorest of the poor. Thus, the sum of each
individual’s P0 is simply the headcount ratio.
The second measure, P1, has a linear and decreasing relation with income. Since
the income gap (income - poverty line) grows larger, more importance is given to the poorest and less to the richest in the poverty measure.
The last measure quantifies the aversion of the society towards poverty, from
figure 2 we see that P2 is strictly convex in income. This implies that the measure
attaches greater importance to the poorest and less to the wealthy in a quadratic fashion.
Pα
1 P0
P1
P2
Poverty line Income
figure 2 Individual Poverty Measures (source: Ravaillon, M. (1996))
As for the poverty line in equation (2), it is determined by the model. The poverty line is represented by the value of an exogenous basket of goods composed of basic nutritive goods that ensure sufficient food energy and other essential non-food goods. This approach is inspired by the “fundamental needs” method discussed in Ravaillon (1996). Specified in this manner, the poverty line is endogenous and depends on the price of each good. If the value of a basket increases following an external shock, the poverty
line will increase (shift to the right). Ceteris paribus, the number of poor in the household group will increase.
4 A General Equilibrium Model of an Archetype of Developing Country
The general equilibrium model presented is inspired by the framework of the Decaluwé et al. (1995) models which in turn follows the guidelines put forward by the Shoven and Whalley models (1972, 1984). This model represents a small open economy characterizing a developing country that has no influence on the international markets.
The model is described as a six sector model (traditional agriculture, export crop, mining, industry, service and administrative service). Land, agricultural capital, capital, unskilled labour and skilled labour are the five primary factors of production employed by the branches. As mentioned in the first part of the paper, households are aggregated into six groups. The geographical location of a household and the origin of their income or occupation defines the groups. For example, a rural household has the characteristics of living in rural areas and possesses unskilled labour.
Production and employment
The production is presented as a Leontief function between the intermediate consumptions and the value added for each sector. Value added is modelled by nested CES between primary factors. The structure of these nested CES differs by sectors. As it is shown in figure 3, the agricultural branches, we posit a CES and a Cobb Douglas that combine the primary factors at the first level of the value added. The first is a CES between the unskilled labour and the skilled labour and the second is a Cobb Douglas between agricultural capital and land. At the second level of the nest, we have a CES between composite capital and composite labour. For the non-agriculture (industry, mining, service and administrative service) branches, we have the same relationship between the unskilled labour and the skilled labour at the first level of the value added. At the second level, the composite labour of the first nest is linked to capital by a CES. As for the factor mobility, the non-agriculture capital is fixed by sector, the agricultural capital is mobile between the agricultural sector, skilled and unskilled labour are mobile between branches but cannot migrate between labour categories, i.e. an unskilled worker cannot be hired as a skilled labour and vice versa.
Other sector Agricultural sectors XS XS LF LF VA CI VA CI io io CES CES LD KD CIJ LD KT CIJ CES CES CD LNQ LQ LNQ LQ KD Land figure 3 Incomes and Savings
The households receive their income from primary factor payments and transfers from the government. From this income, we can derive the disposable income by subtracting the direct taxes collected by the government. Saving and total consumption are then derived by a fixed proportion of the disposable income. A fixed share of capital and land remuneration determines the firm’s income. The firm’s saving is equal to its own income. Government revenue is generated from direct taxes collected on household income, indirect taxes on domestic goods and taxes levied on imports. The state saving is obtained from the difference between it’s income and it’s expenditures. These expenditures are composed of transfers made to other agents and public consumption.
Demand
The households’ expenditure functions are derived (utility maximisation problem) from a Stone-Geary utility function or a Cobb-Douglas linear expenditure system (CD-LES). This type of utility function restricts the households to consuming a basket of goods
generally referred to as basket of subsistence goods 5.
As for the intermediate demand, it represents the sum of intermediate consumption by the production branches. The investment demand for a good is presented as a fixed value of total investment.
5 The minimum consumption of a good by one household has been derived using the Frisch parameter and the income elasticity. For a detailled presentation, the interested reader is invited to consult Dervis, De Melo and Robinson (1982).
Trade
In this model, we follow the Armington (1969) approach by supposing an imperfect substitution between domestic and import goods. As for export, a constant elasticity of transformation characterises the facility of a producer to change markets. Following a change in the relative price of domestic and export goods, the producer is able to change markets at a degree expressed by the elasticity of transformation.
The current account balance representing the rest of the world’s savings is
presented as the difference between the import value and export value.6
Equilibrium
Three equilibrium conditions are respected in the model. The first condition implies the equilibrium between the demand for primary factors and it’s supply, namely one market for skilled labour, one for unskilled labour and one for agricultural capital. There is no market clearing condition for non-agricultural capital since it is immobile The second condition dictates the equilibrium between total investment and total savings. For the third market clearing condition, the domestic demands for each commodities are equal to their respective supply.
Closure
Since the economy has no impact on international markets, the world price of import and export are exogenous to the model. The current account balance and the nominal exchange rate are also exogenous to the model. Furthermore, government consumption and its transfers to households are exogenous. As last closure condition, the primary factor supplies are all exogenous to the model. In this model, both types of labour and agricultural capital are mobile between sectors. Land and capital are specific to each branch.
5 Social Accounting Matrix
The social accounting matrix (SAM) of an archetype developing African economy used in this paper is based on the SAM presented by Decaluwé and Thorbecke (1998). In our case, we adapted the SAM as to take into account the particularities of our study. We count two major modifications to the SAM. The first is the desegregation of the agricultural sector into a traditional agriculture sector and an export crop sector. With this aggregation we will have a better understanding of the effects of a trade shock on the agricultural sectors and the rural households. The second modification is the inclusion of a firm in the SAM. The SAM is presented in appendix A.
As to appreciate the results in the subsequent section, we present in the following tables the income characteristics of the households groups. In table 3, the income composition is displayed for each category.
Table 3: Share of factorial payments to household groups
Unsk. L Skilled L Capital Land Transfers Total
Rural workers 91.94% 8.06% 100% Small Rural landowners 65.72% 21.28% 13.00% 100% Large Rural landowners 7.45% 13.89% 50.19% 28.47% 100%
Urban low income 80.17% 16.06% 3.77% 100%
Urban high income 39.92% 60.08% 100%
Capitalists 27.94% 72.06% 100%
As we can observe in table 3, the income composition of each household group is related to their social classification. The incomes of the rural workers, the small rural landowners and urban low income are mostly composed of unskilled labour payments and the composition of the large landowner, the urban high income and the capitalist household income is principally based of capital payments.
In table 4, we present the share of the productive factors in the value-added for each branch of production. The agricultural (traditional and export agriculture) and services (services and public service) sectors are mostly intensive in unskilled labour and the industrial (mining and industries) sectors intensive in the capital primary factor. Skilled labour is used more intensively in the public services branch and in the mining branch. As for land, only the agricultural branches share the resource.
The effect of a trade shock on household income funnels through the sector for which the household productive resources are employed. Studying tables 3 and 4, we can see that a shock on the agricultural sectors would have a greater impact on rural household income than on the capitalist’s income.
Table 4: Share of the primary factors in the value-added
Agriculture Export Agriculture
Mining Industries Services Public service Unskilled Labour 45.48% 39.32% 8.1% 30.85% 30.61% 55.57% Skilled Labour 0.56% 4.85% 30.41% 7.01% 10.2% 41.96% Capital 8.96% 14.56% 61.49% 62.14% 59.2% 2.47% Land 45.00% 41.26%
6 Results
Two simulations are performed on the model’s base year equilibrium. The first is a reduction in the world price of the export crop on the international market and the second is an import tariff reform. In the following lines, we discuss the effect of these simulations and how they trickle to the household income distribution and poverty
measures. To analyse the impact of a change in household poverty levels, we use the Pα
measures presented in section four.
The first simulation consists of implementing a 30% decrease in the world price of the export crop. This reduction has a direct repercussion on the export agriculture sector. The production of this sector declines by 35.75%. The primary factors employed by this sector at the base year are now reallocated in other branches. Consequently, this reallocation increases the production of the other sectors. However, the nominal GDP at factor price falls by 5.88% and the real GDP decreases only by 0.23%. We link this fall to the decrease in the primary factor prices. In the case of agricultural land, the factor price decreases by 55.80%. Land being the primary factor used intensively in the agricultural production, a shock on this sector depresses the rate of return of land. This effect is amplified by the constraint for which land is specific to each agricultural branch. No reallocation is allowed for this factor, only the rate of return adjusts to the shock. The return of agricultural capital also diminishes considerably with a decrease in the world price of the export crop (-18.62%). As the other two primary factors, the wage of the unskilled and skilled labour also decreases. The wage of the unskilled labour falls by 6.56% and the wage of the skilled labour by 3.83%. Since the unskilled labour represents 39% of the value added in the export agriculture sector versus 5% for the skilled labour, the variation in the first is greater. However, the effects on wages are attenuated by the mobility of the two types of labour between sectors.
The decrease in these factor prices results directly into a fall in household income. As we can observe in table 6, the mean income of each group decreases. The two households affected the most by the shock are the small and large landowner households with a fall of 6.93% and 6.91% respectively. This is a consequence of the drastic drop in the rate of return of land and agricultural capital since they represent 34.3% of the small land owner household income and 78.7% of the large landowner household income.
As for the rural household and the urban low-income household, the decline in their income is mainly a consequence of the decrease of the unskilled wage since the share of their income originating from the unskilled labour salary represents 91.9% and 80.2% respectively. The earnings of the urban high-income household and the capitalist household also decrease. Their income drops by 4.09% and 4.14%. The decline in the household’s earnings is presented by a proportional horizontal shift to the left of the income distribution. The horizontal shifts for each group of household are presented in figures 4a through 4f.
Table 5: Simulation Results
Variables Base Simulation 1 : 30% decrease
in the world price of export agricultural crop (% change of base) Simulation 2 : 50% decrease in import tariff (% change of base) GDP nominal 4462.30 -5.88 -1.56 GDPreal 4462.30 -0.230 0.551 Xsagriculture 1219.50 3.289 -1.034 Xsexport agriculture 281.00 -35.748 2.70 Xsmining 1042.40 2.243 2.70 Xsindustry 2330.10 0.567 -1.37 Xsservice 1435.90 1.189 -0.18 Xsadministrative service 594.00 1.170 0.72 Yg 679.00 -5.10 -12.54
Ydhrural (nomimal) 235.60 -6.03 -1.21
Ydhsmall landowner(nomima)l 1142.60 -6.93 -1.46
Ydhlarge landowner(nomima)l 968.80 -6.91 -1.69
Ydhurban low income(nomimal) 504.50 -5.94 -1.31
Ydhurban high income(nomimal) 539.50 -4.09 -1.67
Ydhcapitalist 639.20 -4.14 -1.65 Exagriculture 181.20 9.94 1.96 Exexport agriculture 231.00 -37.97 3.24 Exmining 535.00 5.87 2.27 Exindustry 195.00 6.36 2.47 Exservice 110.00 6.45 1.75 Magriculture 759.80 -5.20 0.62 Mindustry 296.60 -5.94 8.66 Mservice 100.00 -4.67 -0.49 LQagriculture 2.250 -1.481 0.513 LQ export agriculture 5.000 5.128 -56.789 LQmining 72.300 -3.435 5.217 LQindustry 53.900 -0.141 -1.080 LQservice 48.850 2.088 0.521 LQadministrative service 101.100 1.302 -0.610 LNQ agriculture 487.333 -1.892 3.744 LNQ export agriculture 108.000 4.690 -55.400 LNQindustry 51.333 -3.837 8.600 LNQmining 632.267 -0.557 2.100 LNQ service 390.933 1.663 3.752 LNQ administrative service 357.067 0.880 2.585 Pm service 1.00 - -Pqagriculture 1.06 -3.65 -4.01 Pq export agriculture 1.11 -18.08 -2.71 Pqmining 1.08 -6.54 -6.80 Pqindustry 1.07 -4.65 -3.71 Pqservice 1.06 -4.77 -1.07 wq 2.00 -3.83 -1.69 wnq 0.75 -6.56 -1.31 Ra 1.00 -18.62 -1.26 rtagriculture 1.00 -3.13 -3.04 rtexport agriculture 1.00 -55.80 2.99 rmining 1.00 0.72 -4.76 rindustry 1.00 -4.78 -1.81 rservice 1.00 -3.38 0.18 radministrative service 1.00 -4.37 -0.52
Figure 4a-4f: Effect of a 30% reduction in the world export price of the export agriculture crop on income distribution
10 20 30 40 Income 0.01 0.03 0.05 0.07 f(Income) 10 20 30 40 50 Income 0.01 0.03 0.05 f(Income)
Figure 4a : Income distribution rural households Figure 4b : Income distribution small landowner households
20 30 40 50 Income 0.02 0.04 0.06 f(Income) 10 15 20 25 30 35 40 Income 0.02 0.04 0.06 0.08 f(Income) 10 5
Figure 4c : Income distribution large landowner households Figure 4d : Income distribution urban low income households
20 30 40 50 60 Income 0.01 0.03 0.05 f(Income) 10 20 40 60 80 100 120 140 Income 0.01 0.02 0.03 f(Income)
Figure 4e : Income distribution urban high income households figure 4f : Income distribution capitalist households
Since the poverty line is endogenous a poverty line is redrawn to consider the ex-post situation. The changes in the poverty line are presented in table 6. For the first simulation the poverty line decreases by 4.4%. This reduction is the consequence of a fall in the consumption price of the basket of goods, which determines the poverty line.
With an ex-post distribution and a new poverty line, we can study the Pα class measures
each simulation in appendix B. The integral of these graphs corresponds to the value of the respective measures presented in table 6.
For the headcount ratio, the P0 increases for all household groups. The rural
household remains with the highest headcount ratio with 92.9% of the population below the poverty line. Compared with the base year, this represents a 0.4% improvement in the headcount ratio. This reduction represents the only improvement of all the groups. This is explained by the poverty line reduction which dominates the reduction in income of the household groups. We find the highest relative increase in the urban high-income household. The ratio increases from 0.5% to 0.8% after the increase in the price of the export crop.
Table 6: Poverty Measures for the Base Year and Simulations
Rural Household s Small Landowner Households Large Landowner Households Urban Low-Income Households Urban High-Income Households Capitalist Households social Pα alpha=0 base 0,933 0,361 0,194 0,577 0,005 0 0,380 Simulation 1 0,929 0,396 0,245 0,600 0,008 0 0,407 (-0,4%) (9,7%) (26,4%) (4,0%) (60,0%) - (7,2%) Simulation 2 0,923 0,348 0,183 0,546 0,005∗ 0 0,367 -1,0% -3,7% -5,4% -5,3% -3,1% - -3,4% alpha=1 base 0,443 0,078 0,021 0,093 0,00019 0 0,104 Simulation 1 0,454 0,096 0,032 0,106 0,00038 0 0,116 2,5% 22,9% 50,3% 13,7% 95,6% - 11,4% Simulation 2 0,434 0,076 0,020 0,086 0,00019∗ 0 0,100 -2,0% -3,3% -5,2% -7,8% -1,1% - -13,2% alpha=2 base 0,249 0,024 0,004 0,020 0,00001 0 0,045 Simulation 1 0,263 0,033 0,006 0,025 0,00003 0 0,051 5,7% 37,1% 77,2% 23,7% 138,6% - 13,8% Simulation 2 0,243 0,024 0,003 0,018 0,00001∗ 0 0,043 -2,4% -2,8% -4,9% -9,8% 1,0% - -3,1% base 13,6 27,8 29,9 23,3 41,5 117,7 Mean Income Simulation 1 12,7 25,8 27,8 21,9 39,8 112,9 -6,0% -6,9% -6,9% -5,9% -4,1% -4,1% Simulation 2 13,4 27,3 29,4 23,0 40,8 115,8 -1,2% -1,5% -1,7% -1,3% -1,7% -1,7% base 24,0 24,0 24,0 24,0 24,0 24,0 Poverty Line Simulation 1 23,0 23,0 23,0 23,0 23,0 23,0 -4,4% -4,4% -4,4% -4,4% -4,4% -4,4% Simulation 2 23,3 23,3 23,3 23,3 23,3 23,3 -3,0% -3,0% -3,0% -3,0% -3,0% -3,0% ∗
Results are identical to the base year data due to rounding of the figures
As oppose to the headcount measure, the income gap increases for all households.
The P1 for the urban high-income household increases to 0.00038, an increase of 95.6%.
However, the rural household remains with the highest income gap at 0.454. The rural household has the smallest relative increase in the income gap measure of all the household groups (2.5%).
The same is true for P2, the rural household has the smallest relative increase and
the urban high-income the highest. Nonetheless, the rural household has the highest value with 0.263 and the capitalist household the smallest at 0.0.
In table 6, an aggregate poverty measure for the three class of Pα are presented.
These social poverty measures are a weighted sum of the households’ Pα.7 As we can
clearly observe the social poverty measures of the three class increases with a decline in the world price of the country’s export crop.
In most cases stated in the above discussion the effect pertaining to the shift in the poverty line do not counter balance the income effect. The only case for which the shift
of the poverty line is greater than the income effect is the P0 of the rural household. Only
in this case does than poverty measure improves following the negative trade shock.
Simulation 2
For the second simulation, an import tariff reform is simulated on the archetype model. This reform consists of implementing a 50% reduction in import tariffs on all imports. This policy reduces the domestic price for imports competing with the traditional agriculture (-5.06%) and the industrial (-10.01%) sectors. With a fall in the import price, the agents substitute their consumption of domestic products for import goods. This in turn favours a decline in the consumption price of the domestically produced goods coming from the traditional agriculture and industrial sectors. The decline in the demand of the domestically produced goods of the two concerned sectors will force the branches to redirect to the export market. The exports for the agricultural branch increase by 1.96% and the exports for the industrial branch by 2.47%. Since the export market did not completely absorb the fall in the domestic demand, these branches respectively reduce their production by 1.03% and 0.18%. The resources released by this fall of activity increases the production of almost all the other branches; exception made for the mining sector. The mining branch reduces its production by 1.37%. This is a consequence of the combined fall of the intermediate demand for the mining product coming from the industrial production and the investment demand for the mining product.
With the fall in almost all of the primary factor prices, the nominal GDP at factor cost decreases by 1.56%, however the real GDP increases by 0.55%. The fall in the factor prices also has a negative effect the households’ incomes. The large landowner household has the largest decrease with a variation of 1.69% and the rural household has the smallest decrease with 1.21%.
As in the first simulation, the ex-post income distributions are plotted over the base distribution in figures 5a to 5f. Again, the fall in the consumption price of all the goods reduces the poverty line (shifts to the left). With these results, new poverty levels are presented in table 6.
In this case all headcount ratios, except for the capitalist household for which the measure remains non-existent, improves following a fall in the import tariffs. Thus, the shift in the poverty line is greater than the fall of income. The fall of the consumption
7 household
h social n P
prices more than compensate the fall of income in this poverty measure. With a P0 at
0.0183, the large landowner household income has the highest relative decrease with a
fall of 5.4%. The smallest relative decrease of the P0 measure is ascribed to the rural
household with a fall of 1.0% in this measure.
As the headcount ratio, the income gap measures decreases for all households (exemption made for the capitalist household). However, these improvements are less important for the rural household and the urban high-income household. The rural
household’s P1 decreases to 0.434 (-2.0%) and the one for the urban low-income falls by
1.1%. The urban low-income has the biggest improvement with an increase of 7.8%, All households except the urban high-income household and the capitalist
household reduce their poverty level when measured with the P2. The poverty level for
the urban high-income household increase by 1.0% and the level for the capitalist household remains unchanged. The urban high-income household has the largest relative decrease at 0.018 (-9.8%).
As for the social poverty levels presented in table 6, the headcount ratio and the income gap declines by 3.4% and 13.2% respectively. Here, the reductions in import tariffs are beneficial to the social poverty level. The same is true when society has a greater aversion towards poverty. In this case, the social poverty level declines slightly to 0.043 (-3.1%).
Figure 5a-5f: Effect of a 50% reduction in import tariffs of all imports
10 20 30 40 Income 0.01 0.03 0.05 0.07 f(Income)
10 20 30 40 50 Income 0.01 0.03 0.05 f(Income)
figure 5b : Income distribution small landowner household
20 30 40 50 Income 0.02 0.04 0.06 f(Income) 10
figure 5c : Income distribution large landowner household
15 20 25 30 35 40 Income 0.02 0.04 0.06 0.08 f(Income) 5 10
20 30 40 50 60 Income 0.01 0.03 0.05 f(Income) 10
figure 5e : Income distribution urban high income
20 40 60 80 100 120 140 Income 0.01 0.02 0.03 f(Income)
figure 5f : Income distribution capitalist
Conclusion
In this paper, we try to overcome some of the austerity present in previous studies for which poverty is analyzed using a computable general equilibrium model. We depicted the flexibility of a Beta function to represent various types of households. Contrary to the lognormal and the Pareto, the Beta is more rigorous as to the squewess and bi-modal forms it can adopt. The modeler should less likely reject a household group by cause of inappropriate results of a squewness and kurtosis test.
Also, we proposed an endogenous poverty line tied to a change in the price of the fundamental needs represented by a baskets of goods as to reflect the realities of external shock or policy reforms on the cost of living. It implies that one can be poorer without any change or an increase in income. In fact, results indicate that the change in the poverty line has a significant effect on the poverty levels. In the tariff reform simulation, the change in the poverty line is important enough to counter balance the drop in income
of the rural household in almost every case. Thus, the Pαimproves for most households.
In the first simulation, only the P0 for the rural household improves with a drop in the
price of the export crop. However, the poverty line effect attenuates the deterioration in
One major difficulty remains when using CGE model in study poverty analysis. As discuss by Dervis, De Melo and Robinson (1982), the endogenous characteristic of the income variance remains a major difficulty in this type of modeling. The modeler resorts to a given rule to distribute a gain or loss of income in an ex-post situation. When modelers circumvent this difficulty, the analysis of poverty using a CGE will be an indisputable tool.
Bibliography
Adelman, I, S. Robinson (1979), Income Distribution Policy: A Computable General
Equilibrium Model of South Korea, in Adelman, I, The selected essays of Irma Adelman.
Volume 1. Dynamics and income distribution. Economists of the Twentieth Century Series. Aldershot, U.K., pp. 256-89.
Armington, P.S. (1969), A Theory of Demand for Products Distinguished by Place of
Production, IMF Staff Paper no 16, pp. 159-176.
Atkinson, A. B. (1987), On the Measurement of Poverty, Econometrica, vol. 55, no 4, pp.
749-764.
Azis, I. (1997), Impacts of Economic Reform on the Rural-Urban Welfare: A General
Equilibrium Framework, Review of Urban and Regional Development Studies, 9(1), pp.
1-19.
Benjamin, N. (1996), Adjustment and Income Distribution in an Agricultural Economy: A
General Equilibrium Analysis of Cameroon, World Development, 24(6), pp. 1003-13.
Blackwood, D. L. and R. G. Lynch (1994), The Measurements of Inequality and Poverty:
A Policy Maker’s Guide to the Literature, World Development, 22(4), pp. 567-578.
Bordley, R. F., J. B. McDonald and A. Mantrala (1996), Something New, Something Old:
Parametric Models for the Size Distribution of Income, Journal of Income Distribution,
6(1), pp. 97-102.
Bourguignon, F. and G. Fields (1997), Discontinous Losses from Poverty, Generalized
α
Chia, N. -C., S. Wahba and J. Whalley, Assessing Poverty-Reduction Programmes: a
General Equilibrium Approach, Journal of African Economies, 3(2), pp. 309-338.
Decaluwé, B., M. –C. Martin and M. Soussi (1995), école PARADI, Université Laval. Decaluwé, B. and E. Thorbecke, Social Accounting Matrices and Computable General Equilibrium Models in Poverty Analysis, AERC Technical Notes, forth coming.
De Janvry, A., E. Sadoulet and A. Fargeix (1991), Ajustement et équité en Équateur, Series: Ajustement et équité dans les pays en développement, OCDE, Paris.
Dervis, K, J. DeMelo and S. Robinson (1982), General Equilibrium Models for
Development Policy, Cambridge University Press, London, pp. 1-526.
Fortin, B., N. Marceau and L. Savard, Taxation, wage controls and the informal sector, Journal of Public Economics, 66, pp. 293-312.
Foster, J., J. Greer and E. Thorbecke (1984), A Class of Decomposable Poverty
Measures, Econometrica, 52(3), pp. 761-766.
Johnsons, N. L. and S. Kotz (1970), Continuous Univariate Distribution, Vol. II, Wiley, New York.
Ravaillon, M. (1996), Comparaisons de la pauvreté: concepts et méthodes, LSMS no
122, the Word Bank, Washington, D.C..
Rimmer, M. T. (1995), Development of a Multi-Household Version of the Manash Model, Centre of Policy Studies and the Impact Project Working Paper OP-81.
Shoven, J.-B. and J. Whalley (1972), A General Equilibrium Calculation of the Effects of
Differential Taxation of Income from Capital in the U.S., Journal of Public Economics, 1,
pp. 281-322.
Shoven, J.-B. and J. Whalley (1984), Applied General Equilibrium Models of Taxation
and International trade: An Introduction and Survey, Journal of Economic Literature, 22,
pp. 1007-1051.
Thorbecke, E. (1991), Adjustment, Growth and Income Distribution in Indonesia, World Development, 19(11), pp. 1595-1614.
Appendix A: Social Accounting Matrix for Archetype African Developing Country
Table A1 :Social Accounting Matrix for Archetype African Developing Country
Factors Households Activities Commodities
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Unskilled labour 1 365,5 81,0 38,5 474,2 293,2 267,8 1 520,2
Factors Skilled labour 2 4,5 10,0 144,6 107,8 97,7 202,2 566,8
Capital 3 72,0 30,0 292,4 955,3 567,1 11,9 1 928,7 Land 4 361,6 85,0 0,0 0,0 0,0 0,0 446,6 Rural workers 5 228,0 0,0 0,0 0,0 20,0 248,0 Rural land-owners (small) 6 790,5 0,0 255,9 156,3 0,0 1 202,7
H'holds Rural land-owners (large)
7 76,0 141,7 511,8 290,3 0,0 1 019,8
Urban low income 8 425,7 0,0 85,3 0,0 20,0 531,0
Urban high income 9 0,0 226,7 341,2 0,0 0,0 567,9
Capitalists 10 0,0 198,4 511,8 0,0 0,0 710,2 Entreprise 11 222,7 Agriculture 12 1 038,3 0,0 0,0 0,0 181,2 1 219,5 Export Africulture 13 50,0 231,0 281,0 Activities Mining 14 0,0 507,4 0,0 0,0 535,0 1 042,4 Industries 15 0,0 0,0 2 135,1 0,0 195,0 2 330,1 Services 16 0,0 0,0 0,0 1 325,0 110,0 1 435,0 Public Services 17 0,0 0,0 0,0 594,0 0,0 594,0 Agriculture 18 95,0 412,7 271,9 171,6 97,1 32,4 204,8 0,0 323,3 0,0 0,0 0,0 274,9 1 883,7 Exp. Agr. 19 0,0 0,0 0,0 0,0 0,0 0,0 40,0 10,0 50,0 Comm. Mining 20 0,0 0,0 0,0 0,0 0,0 0,0 0,0 19,3 43,1 0,0 0,0 0,0 445,0 507,4 Industries 21 83,1 402,8 384,2 191,7 242,4 153,1 186,1 30,0 337,5 301,7 143,3 0,0 0,0 50,0 2 505,9 Services 22 57,5 291,0 271,9 141,2 146,1 98,6 0,0 173,6 43,1 247,6 76,5 471,9 0,0 2 019,0 Government 23 12,4 60,1 51,0 26,5 28,4 71,0 25,0 5,0 36,5 81,6 86,1 35,6 85,6 0,0 74,2 0,0 679,0 Accumulation 24 0,0 36,1 40,8 0,0 53,9 355,1 222,7 167,1 -95,8 779,9 ROW 25 759,8 0,0 296,6 100,0 1 156,4 Total 1 520,2 566,8 1 928,7 446,6 248,0 1 202,7 1 019,8 531,0 567,9 710,2 222,7 1 219,5 281,0 1 042,4 2 330,1 1 435,0 594,0 1 883,7 50,0 507,4 2 505,9 2 019,0 679,0 779,9 1 156,4
Appendix A : The General Equilibium Model
I. List of Symbols
Indices
Activities: agr Agriculture
agex Rent agriculture
min Mining
ind Industry
ser Services
as Administrative services
Commodities: agr Agriculture
agex Rent agriculture
min Mining
ind Industry
serv Composite services (as, ser)
Sets:
I { agr, agex, min, ind, ser, as } Production activities
AG { agr, agex } Agricultural activities
IN { min, ind, ser, as } Non-agricultural activities
MER { agr, agex, min, ind, ser, } Exporting activities COM { agr, agex, min, ind, serv } Commodities
Households: mrur Rural households (landless)
mls Small agricultural land owners households
mll Large agricultural land owners households
muli Low income urban households
muhi High income urban households
cap Capitalist households
H {mrur, mls, mll, muli, muhi, cap}
Parameters
CES Elasticity of substitution of VA σi
CES Substitution parameter of VA ρi
CET Distributive share of VA δi
CES Scale parameter of VA Bi
CES Elasticity of substitution of LD σil
CES Substitution parameter of LD l
i
ρ
CET Distributive share of LD l
i
δ
CES Scale parameter of LD l
i
Cobb-Douglas elasticity for KT
ag
α
Cobb-Douglas scale parameter for KT
ag
A
Cobb-Douglas elasticity for Dserv d
α
Cobb-Douglas scale parameter for Dserv d
A
Share of commodity I in household h consumption c
com h,
β
Minimal consumption (in quantity) of commodity
com
ϖ
Share of commodity in public consumption βcomg
Household marginal propensity to save
h
mps
Share of commodity i in total investment βcomI
Activity i's share in total production x
i
β
Household share of capital income λkh
Household share of land income λth
Household share of skilled labour income λqh
Household share of unskilled labour income λnqh
Input-output coefficients aijcom,j
Share of value added in total output vi
Household income tax rate tyhh
Indirect tax rate txi
Import duty rate tmcom
CET scale parameter BTmer
CET transformation parameter T
mer
ρ
CET distributive share δmerT
CET elasticity of transformation T
mer
σ
CES scale parameter BcomS
CES substitution parameter S
com
ρ
CES distributive share δcomS
Endogenous Variables
PRICE
Wage rate wi
Skilled wage rate wq
Unskilled wage rate wnq
Value added price Pvai
Producer price Pi
Rate of return on capital
in
r
Rate of return on agricultural capital ra
Rate of return on land
ag
rt
Price of composite capital
ag
Pk
Price of commodities and services Pdi+serv
Price of composite commodities
com
Pq
Domestic price of imports
com
Pm Domestic price of exports
mer
Pe
Producer price index Pindex
PRODUCTION
Value added
i
VA
Total production by activity
i
XS
FACTORS
Agricultural composite capital KTag
Agricultural capital demand
ag KD
Skilled labour demand
i
LQ
Unskilled labour demand LNQi
Composite labour demand
DEMAND
Total household consumption
h
CH
Household h consumption of commodity com
com h
C , Total consumption of commodity i
com
CT
Total investment IT
Consumption of commodity i for investment uses
com
INV
Intermediate demand of commodity i
com INTD
Intermediate consumption of commodity com by activity j
j com
ICJ , Imports (cif vol)
com M
Exports (fob vol) EXmer
Domestic demand for domestically produced commodities Di+serv
Domestic demand for composite commodities
com
Q
INCOME AND SAVING
Total household income
h
YH
Household disposable income
h YDH Firm income YF Government revenue YG Household savings h SH Firm savings SF Government savings SG Indirect taxes i TXS
Revenue from import duties
com
TXM
__________________________________________________________________________
Exogenous Variables
Unskilled labour supply LSNQ
Skilled labour supply LSQ
Non agricultural capital by activity KDin
Agricultural capital stock KA
Land
ag
LAND
Nominal exchange rate e
World price of exports (in foreign currency) Pwecom
World price of imports (In foreign currency) Pwmcom
Current account balance CAB
Government transfer payments to household TGHh
II. EQUATIONS Production 1-i i i v VA XS =
2- ICJcom,j =aijcom,jXSj
Non-agricultural activities
CES between composite labour and capital
3-
[
in(
)
in]
in in in in in in in B KD LD VA δ ρ δ ρ ρ 1 1 − − − + − =Labour demand derived from 3.
4-(
)
(
)
− − + − = in in in in in in in in in in in r w B VA LD ρ σ δ δ δ δ 1 1 1 1 CES between qualified and unqualified labour5-l in l in l in in l in in l in l in in B LNQ LQ LD ρ ρ ρ δ δ 1 1 − − − − + =
Labour demand derived from 5.
6-( )
( )( )
l in l in l in l in wnq wq l in l in l in in in B LD LQ ρ σ δ δ δ δ 1 1 1 1 + − = − − Factor prices 7-in in in in in in KD LD w VA Pva r = − 8-in in in in LD wnqLNQ wqLQ w = + Agricultural activitiesCES between composite labour and capital
9-
(
)
( )
ag ag ag ag ag ag ag ag B KT LD VA δ ρ δ ρ ρ 1 1 − − − + − =Composite labour demand derived from 9
10-(
)
(
)
( )
ag ag ag ag ag ag Pk w ag ag ag ag ag B VA LD ρ σ δ δ δ δ 1 1 1 1 + − = − −C-D between agricultural capital and land 11- ag ag ag ag ag ag A KD LAND KT = α 1−α
Agricultural capital derived from 11.
12-ra KT Pk KDag =αag ag ag
CES between qualified and unqualified labour
13-l ag l ag l ag ag l ag ag l ag l ag ag B LNQ LQ LD ρ ρ ρ δ δ 1 1 − − − − + = 14-
(
)
( ) − − + − = l ag l ag l ag l ag wnq wq l ag l ag l ag ag ag B LD LQ ρ σ δ δ δ δ 1 1 1 1 Factor prices 15-ag ag ag ag ag ag KT LD w VA Pva Pk = − 16-ag ag ag ag ag LAND raKD KT Pk rt = − 17-ag ag ag ag LD wqLQ wnqLNQ w = +Income and Savings 18-h ag ag ag t h ag ag in in in k h i i q h i i nq h h TGH LAND rt KD ra KD r LQ wq LNQ wnq YH + + + + + = ∑ ∑ ∑ ∑ ∑ λ λ λ λ 19- ( ) h h h YH tyh YDH = 1− 20- + − = ∑ ∑ ∑ ag ag in in in h k h r Kd ra Kd YF 1 λ 21- =
∑
+∑
+∑
com com i i h h hYH TXS TXM tyh YG 22-i i i i tx PXS TXS = 23-com com com com etm Pwm M TXM = 24-YDH SH25- 26-CG TGH YG SG h h− − = ∑
Demand for commodities 27-h h h YDH SH CH = − 28-com mer com com h c com h com com h Pq Pq CH Pq C − + = ∑ϖ β ϖ , , 29-com g com h com h com Pq CG C CT =
∑
, + β 30- =∑
j j com com ICJ INTD , 31-com i com com Pq IT INV = β Prices 32-i i com com com i i i VA ICJ Pq XS P Pva ,∑
− = 33-Pm
Pwm
(
tm
)
e
com com com=
1
+
34-(
mer)
mer mer te e Pwe Pe + = 1 35-com com com com com com Q M Pm D Pd Pq = + 36-ser as as serv serv ser D D Pd D Pd Pd = − 37- Pdas =(
1+txas)
Pas38-(
mer)
mer mer mer mer mer mer XS tx EX Pe D Pd P + + = 139-∑
= i i x i P Pindex β Foreign Trade 40- XSas = Das 41- Dserv = AdDasαd Dser1−αd42-as serv serv d as Pd D Pd D =α 43-
(
)
T mer T mer T mer mer T mer mer T mer T mer mer B EX D XS δ ρ δ ρ ρ 1 1 + − = 44-(
)
mer T mer T mer mer mer mer D Pd Pe EX T mer T mer σ σ δ δ − = 1 45-[
(
)
]
comS S com S com com S com com S com S com com B M D Q δ ρ δ ρ ρ 1 1 − − − + − = 46-(
)
com S com S com com com com D Pm Pd M S com S com σ σ δ δ − = 1 47-mer mer mer com com comM Pwe EX Pwm CAB= ∑ −∑ Equilibrium conditions48- Qcom=CTcom+INTDcom+INVcom
