Results from the ''Dual-Dual'' CGE Model and their Interpretation :Poverty Analysis in a Generic CGE Model for South Asia

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 developing economy with not only the traditional and modern sectors but also a kind of dualism within each of these sectors in terms of formal/informal dichotomy.³⁰ Furthermore, the process of development for economies at a higher level of development may modify the traditional sector further in the direction of a more market-based modern sector.

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)³¹. 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) 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.³² 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. I have modified the model on the production side by replacing the Cobb-Douglas production functions of the Stifel-Thorbecke model with more general CES production functions. The trade liberalization policies' impact on poverty reduction are given for this new, CES specification in this paper.As is well known, on the production side, the latter specification allows a choice from a much wider range of elasticities than does the Cobb-Douglas production function. On the distribution side, Cobb-Douglas production functions with the unitary elasticity of substitution imply fixed factor shares. Thus CES functions( of Cobb-Douglas production functions is a special case) allow more flexibility on both the production and the distribution sides.Of course, the actual elasticities of sectoral production functions are empirical issues. But for this reason in particular, Cobb-Douglas production functions with the unitary elasticity of substitution may be a priori too restrictive. The equations of the modified model are as follows:

See Representation of Dual-Dual Model with CES Production Functions [ PDF 195.9KB | 2 page ]

The production sectors are specified as CES with the choice of nonunitary³³ elasticities of substitution for the two formal sector commodities in equations 1 and 2. The informal sector commodities also have CES 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 that there are transactions costs in working in the rural formal sector that is captured by this mark up.³⁴

Turning now to the import sector, for 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.

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.³⁵ 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 conditions 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 here. Hence current account balance is assumed to be zero.³⁶ The SAM below in Table 1 [ PDF 98KB | 1 page ] which is largely compiled from data for India below summarizes the relevant information for our generic South Asian economy. Note that in the SAM, the labor and capital are shown in aggregate forms; but in actual modeling exercise these are further disaggregated as discussed during the model description above.³⁷

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. The sources of income poverty can be traced to the sources of income of the various households. Table 2 [ PDF 142.4KB | 1 page ] below gives the factorial sources of household incomes of poor households in the model economy. The numbers are hypothetical and are the same as Stifel- Thorbecke's specifications.

Among all the household groups, rural smallholders have 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 2 [ PDF 142.4KB | 1 page ] shows they derive 75 percent of their income from wages in the unskilled labor market and 25 per cent from capital.

Table 3 [ PDF 145KB | 1 page ] below shows the initial mean incomes and population shares before the policy experiment. This has been created by taking the demographic and other characteristics of households in South Asia---particularly in India and Bangladesh. 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 3 [ PDF 145KB | 1 page ] above, it appears that the mean incomes have a wide range----from 0.92 for the urban informal workers to 3.50 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 (41 per cent of the population) and other households with low education and skills such as rural unskilled, urban informal and urban unskilled comprise about 80% 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 about 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 can not 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:

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

The trade policy experiment involves a tariff reduction that ranges from 87% to below 20%.³⁸ The obvious and immediate effect is a drop in the price of imports and a relative increase in the price of exports.³⁹ In keeping with the shape of the supply curves production rises for exports and falls for the import-competing sector.⁴⁰ Consistent 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 4 [ PDF 81.4KB | 1 page ] below gives 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 in general, both the extent and depth of poverty decline for each group. The largest headcount ratio drop is recorded for the rural unskilled group. Poverty severity also falls for each household group with the exception of the urban unskilled workers. But when the tariff rates fall from 15 to 12 percent, this group benefits as well. In general though, much of the poverty reduction impact of trade liberalization can be reaped earlier. Further reductions leading to a rate below 10 per cent may not have much more of an impact than earlier tariff reductions. One surprise, however, is the largely nonlinear impact of tariff reductions on poverty. Although there is a progressive gain from liberalization, there seems to be a big jump nationally when the rate is in the range of 15 to 18 per cent. However, there is very little change for even lower rates, for example, from 15% to 12%.Given the stylized nature of the exercise, no magical properties need to be attributed to these particular numbers. The general lesson is that tariff reduction will ultimately benefit the poor; but the trickling down process is uneven and may require some time to work through the socio-economic system.

We look at the poverty gap squared measure next. From the results presented in Table 4 [ PDF 81.4KB | 1 page ], it turns out that tariff reduction does lead to a reduction in poverty severity at 18 per cent. However, the change in the national poverty measure is small--- a fall of only one per cent. This is consistent with the observation that trade liberalization may benefit initially those among the poor who are closer to the poverty line than those who are far below. It may leave unchanged the incomes of those who are well below the poverty line. But the good news surely is that when tariffs are sufficiently low, some of the poorest may finally begin to benefit.

Scrutinizing Table 4 [ PDF 81.4KB | 1 page ] carefully, it can be seen that for the various household groups the headcount jump is relatively more significant for several of the rural household groups. In particular, both the rural skilled and unskilled household groups experience significant changes in poverty reduction at the lower tariff rates. For urban unskilled the changes are even larger absolutely but are relatively less dramatic and more monotonic over an entire range of gradually declining tariff schedules.. However, for the poverty gap measure, the poverty reduction effects shown are much smaller for this group. By contrast, the urban skilled household group via higher wages and better employment opportunities experiences a further reduction of about 20% when tariff rates are reduced from 20 to 18 per cent. However, this group has fewer poor households to begin with. Hence, the overall impact on national poverty reduction is small.

In terms of the change in poverty severity measure, the urban unskilled show the greatest improvement. This group is followed by rural unskilled, rural skilled and rural smallholders. Thus an overall average tariff rate reduction target all the way down to the range of 10 to 20 per cent range seems a reasonable trade liberalization policy objective for a South Asian economy from a poverty reduction perspective.

However, a cautionary note needs to be sounded so that there is a sense of realism about the potential of trade liberalization alone to meet the overall poverty reduction targets. Although the positive effect on national poverty is clearly discernible within our model with the results derived from South Asian data, the absolute amount is not as high as it would need to be given the poverty reduction targets of the Millenium Development Goals, for instance. In part this is because of 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. One needs a dynamic model to trace out these movements over time and also to estimate the dynamic benefits of liberalization. This is an important future task although beyond the scope of the present paper.⁴¹

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