Poverty Analysis in a Generic CGE Model: the Dual-Dual Structure

It would indeed be very helpful to the applied policy analysis for poverty reduction if there could be a generic model that could be applied to a number of different policy settings in different countries. Efforts are underway, as we shall see. However, there are some serious obstacles along the way, as subsequent discussion will show. I will try to assess at the end what could be a reasonable use of such generic models.

Among the models mentioned in the previous section, the closest to being a generic model is the Stifel-Thorbecke (2003) model of an archetype African economy. They build a CGE model in order to simulate the welfare effects of trade liberalization. In particular, their effort is directed towards an analysis of the effects of trade liberalization on poverty. They use what can be called a "dual-dual" frame work (Thorbecke, 1993,1994,1997). This corresponds to the characteristics of a mid-level developing economy.²⁴

Briefly, the coexistence and distribution of modern and informal type of activities in both rural and urban areas are taken as basic structural features of the economy in question. According to the authors their modelling approach integrates poverty analysis with CGE proper "… by endogenizing both intra-group income distributions and the nominal poverty line". Following this line of work leads to their being able to assess policy repercussions on both poverty specific to particular socioeconomic groups and on overall national poverty.

The starting point is the dual economy models of Lewis (1954) and Fei and Ranis (1964)²⁵. These pioneering efforts, however, could not or did not take into account the co-presence of dualism within each sector of the two sector models of the dual economy. Erik Thorbecke first raised this issue in 1979 during the course of a National Science Foundation interdisciplinary project on technology and development and Svejnar and Thorbecke (1982) was the first published work on a prototypical of dual-dual technology classification scheme. Khan (1982a,b) and Khan (1983) were applications of this scheme to the energy and textiles sectors in South Korea. Khan (1983) first raised the issue of linking technological dualism to poverty theoretically, following an early observation of Pyatt and Thorbecke (1976). Khan and Thorbecke (1988,1989) were further applications of technological dualism to Indonesia.

In Thorbecke’s later classification a rural/urban dichotomy is combined with traditional/modern technological dualism, leading to a fourfold classificatory scheme. The four broadly defined sectors in this scheme are:

1. subsistence agriculture with traditional labor-intensive technologies, family farms and food crops for domestic consumption;
2. large scale agriculture producing mostly export crops using capital-intensive technology.
3. the urban informal sector defined in an operational manner;
4. modern sector with industry and services in the urban areas.

Poverty analysis in this dual-dual model proceeds along the lines developed by Decaluwé, Bernard, A. Patry, Luc Savard, and Erik Thorbecke (1999). This approach relies on varying prices and a fixed commodity basket to derive an endogenous (nominal) poverty line every time there is a shock resulting in a new equilibrium price vector for the economy. It also uses a beta distribution with varying parameters to capture differences in income distributions that are group specific. Within each group also the parameters can vary, resulting in a new distribution. Standard poverty measures are applied to pre-policy shock and post-policy shock income distributions to derive the impact on poverty. The equations of the model are as follows:

See Representation of Dual-Dual Model [PDF 141kb | 2 pages]

The production sectors are specified as Cobb-Douglas with unitary elasticity of substitution for the two formal sector commodities in equations 1 and 2. The informal sector commodities also have Cobb-Douglas specifications. All commodities are produced under capital constraints. Thus, capital, K, in each sector has an upper bound denoted by a bar above K. The assumption that capital stock is fixed in each sector may be relaxed, but it is in fact, a fairly standard assumption for developing economies.

In the informal sectors each worker receives her average revenue product. Rural small holders may work on common land and these rural farming households may share the total income equally among all the family members. Urban informal workers supply all their labor at the prevailing wage rate. Thus leisure is not an argument in their objective function. This may be defended as an extreme assumption when people are at the margins of subsistence. Equations 5 and 6 show the informal sectors’ income determination.

The total income per unit includes logically the returns also to nonlabor assets for those who own land or capital. Hence, the relevant measure of income is total income per unit from all sources. The profit maximizing rural large landholders ensure that under competitive conditions wages for unskilled workers in the export sector are equal to the marginal revenue product of the unskilled labor they have to hire. Equation 7 reflects this condition.

Equation 8 shows the equilibrium allocation of unskilled labor in the rural informal sector. In equilibrium the rural sector wage rate is below the wage rate in the formal sector by a fixed factor. This reflects the assumption by the authors that there are transactions costs in working in the rural formal sector that is captured by this mark up.²⁶

Turning now to the import sector unskilled workers in the urban area the assumption here is that they get the income per unit of labor in the urban services sector (shown in equation 9) plus a share of the profits as given in equation 10. The profit determination itself is shown in equation 11.

The Harris-Todaro model features regarding rural-urban migration are captured in equation 12. Here, in equilibrium, rural wage must equal the expected wage in the urban sector. In equation 12, the probability of getting a job in the import sector is given by the share of the urban uneducated labor force in that particular sector multiplied by a scale parameter, h.²⁷

Skilled workers are employed only in the formal sectors. Their wages are determined in equations 13 and 14 by their marginal revenue products. We now turn to the determination of incomes for the households.

Household Income Determination:

There are nine types of households. Two in the rural area are landowning households--- large and small. There are also urban capitalists and bureaucrats. The other five are households where the main source of income is from labor.

The rural informal households which are really rural small holders receive their total revenue from production as shown in equation 16. Rural unskilled and skilled households receive their wage incomes as shown in equations 17 and 18 respectively. Equation 19 gives the incomes of the rural large land holders.

Equations 20- 24 show the incomes of the urban households. The working class households receive wage income and the capitalists the profit incomes, in general. The bureaucratic households capture part of the rents from imports by colluding with the rent seekers.²⁸ The formal sector employers (rural large land owners and urban capitalists) are the only savers in the model. They each save a constant fraction of their nominal incomes.

Household demand functions are captured by maximization of Cobb-Douglas utility functions subject to their income constraints. There are 23 such equations (equations 27-49) because the four rural household groups have access to only food and importables. This gives us eight equations. Each of the urban groups has access to three commodities--- food, importables and urban services. This gives another 15 equations. The prices for the three commodities can be used to define an overall deflator.

Foreign Trade:

Imports in this model are the difference between domestic demand and production of import competing sector. Exports can be supplied at the prevailing price up to any quantity under the small country assumption. Thus exports are equal to total output less the savings in the form of exportables of the rural large landholders. Equations 50 and 51 show the import and export demand functions respectively.

Equilibrium conditions for the model as a whole:

There are two sets of equilibrium conditions in the model. First, the labor market equilibrium conditions are given by equations 52 and 53. There is disguised unemployment, as discussed before, but no formal involuntary unemployment. The second set of equilibrium condition given by equations 50 and 51 is that the domestic demand for the informal sector goods and services is matched by domestic supply. Prices in the formal sectors are set by the world market prices The export price is normalized to one. The import price is equal to 1+t, where t is the tariff rate. Exchange rate is held fixed during the particular modelling period. It is clear that the current account balance must be exogenous. In line with our discussion in the previous section, this balance is equal to foreign savings which are assumed to be zero by the authors. Hence current account balance is assumed to be zero.

Poverty Analysis in the Generic Model:

In order to carry out the poverty analysis, it is important to realize that the extent of poverty is unevenly spread across different households. Table 5 [PDF 85kb | 1 page] below gives the distribution of poor households in the model economy.

Clearly, rural smallholders have both the second lowest average income and they have the second highest incidence of poverty. The highest incidence of poverty is found among the urban informal households. As Table 5 [PDF 85kb | 1 page] shows they derive 75 percent of their income from wages in the unskilled labor market and 25 per cent from capital.

Table 6 [PDF 85kb | 1 page] below shows the initial mean incomes and population shares before the policy experiment. This table also shows the headcount measure of poverty rates for each of the household groups that earn at least some labor income. It ignores three household groups, however. The groups thus ignored are rural large landholders, urban capitalists and bureaucrats. The reason is simple. None of these households are assumed to be in poverty, nor does the particular policy shock results in poverty for any of these three groups.

From >Table 6 [PDF 85kb | 1 page] above, it appears that the mean incomes have a wide range----from 0.97 for the urban informal workers to 5.85 for the urban skilled workers. These incomes are scaled relative to the pre-tariff import price which is the numeraire in the model. Among the skilled groups, the richest are in the urban sector. For the unskilled also, the urban unskilled group has the highest income, for reasons explained previously. Rural smallholders (60 per cent of the population) and other households with low education and skills such as rural unskilled, urban informal and urban unskilled comprise 85% of the total population and almost all of the poor come from these groups. Contrarily, households comprising of highly educated and skilled workers account for a mere 10 per cent of the total population and only 0.4% of those below the poverty line come from these groups.

For an adequate analysis of the policy impact on poverty one needs not just the information about the composition of households and their mean incomes, but also on the intragroup income distributions. As mentioned before, the statistical distribution function chosen to fit the various degrees of mean, variance, skewness and other features is the Beta Distribution. This choice allows a certain flexibility. The density functions can be either symmetric or asymmetric. They can also be skewed to the left or to the right. Of course, the choice of parameters that will result in a particular shape of the distribution function cannot be arbitrary, but really should be guided by the actual shapes, or some information regarding these shapes, of the distribution functions for each particular group of households. Here, well-designed and accurate household surveys can lead to a much improved policy analysis. In this particular exercise, the assumption of within group distributional neutrality after the policy shock is maintained. Therefore, the impact on poverty comes from mainly the growth effects of the policy. A second, significant feature, however, is the urban-rural migration after the policy shock. This also affects the poverty reduction possibilities of liberalization, as we will see shortly.

Policy Simulation in the Model and Impact on Poverty:

According to the initial conditions postulated by the authors, at the outset 29% of the population is urban based and 71% rural based. The composition of households according to labor skills is 85% unskilled and 10% skilled. Rural smallholders are the largest group with close to 60% of the total population. Next is the urban informal with 14% of the total population. The urban skilled and rural unskilled each have 7% and the urban unskilled and rural skilled have 5% and 3% of the total population respectively.

The production of food in the rural informal sector makes up half the total output for the entire economy. The urban informal sector produces 10% and formal sector produces 20% of the total output. Finally, the rural export sector produces another 20%.

Prior to the policy experiment of tariff liberalization, the urban skilled workers in the model economy enjoy the highest level of wages. Their wages are more than twice the level of the rural skilled, two and a half times that of the urban unskilled and more than five times that of the other three groups.

The trade policy experiment involves a tariff reduction from 40% to 20%. The obvious and immediate effect is a drop in the price of imports and a relative increase in the price of exports.²⁹ In keeping with the shape of the supply curves production rises for exports and falls for the import-competing sector.30Consistent with this, demand for both skilled and unskilled labor drops in the urban importables sector, and rises in the rural exportables sector. There is also a fall in the wages in the former sector, and a reverse migration out of this sector in the urban area to the export sector in the rural area. For this particular policy experiment, in the new general equilibrium, the share of urban skilled workers falls by 9%. At the same time the share of rural skilled workers rises by about 22%. Correspondingly, there is also a movement of the unskilled workers from the urban to the rural area as well. Finally, the fall in the aggregate income in the urban formal sector reduces effective demand for the urban services sector as well, pushing out the urban informal sector workers towards the rural area also.

Table 7 [PDF 98kb | 1 page] and Table 8 [PDF 117kb | 1 page] give the results for poverty reduction. Two implicit assumptions underlie these results. First, individuals who migrate take on the socio-economic characteristics of the group in which they end up. Second, both the groups---i.e., the group from which the individual migrates and the group to which the individual worker migrates--- still have the same income distribution as before the migration.

Under the assumptions, the results within the model show that poverty depth declines for each group. The largest drop is recorded for the rural unskilled group. Poverty severity also falls for each household group with the exception of the urban unskilled workers.

Table 8 [PDF 117kb | 1 page], which shows a decomposition of the changes in national poverty into the changes within the group and into the effects of migration between the groups, reveals that the decline in poverty among the rural smallholders accounts for most of the fall in national poverty. It can be recalled that about sixty per cent of the total population comes under this category. Hence, the result is to be expected. However, what could not have been anticipated is the extent by which the structure of wages and migration can dampen the poverty reduction impact of SAPs--- in this case of trade liberalization. As Stifel and Thorbecke point out:

In the absence of migration the reduction in poverty resulting from the trade reform would have been significantly overestimated. This results from the unskilled and skilled workers losing jobs in the import sector and migrating to the rural areas where they earn much lower wages. Note that the migration result is negative despite the fact that 1.6% of the population migrates out of the poorest socio-economic group, the urban informal sector, into the better paying export sector. (Italics added)³¹

Although the positive effect on national poverty is still discernible, there are migrations taking place from both high paying to low paying and vice versa. The net effect is smaller than it would have been if only low paying to high paying job migration were taking place.

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