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The dynamics in a typical rural community are an irony between simplicity in rural life and the complexity of the economic system that is operating. The literature offers diverse theories and perspectives in trying to explain the rural economy. There seems to be a cycle over the years among these theories, postulated, reinvented, reformulated, refuted in some cases, and emerging again in recent literature. Lewis (1984) postulated that in the rural economy, growth is triggered by the initiation of trade. Farmers are producing not just for consumption but also for the demand in other communities. This is a valid assumption once productivity had exceeded the threshold for local needs. Otherwise, if production level is still below the threshold, marginalization and subsequent exposure to vulnerability will dominate rural production with growth hardly manifesting, if not remaining impossible. Intensive intervention will be needed to push the farmers initially to cross the threshold for growth. Growth will naturally push economic activities towards diversity at the community level and possibly (but not necessarily) specialization at the household level.
In a growing rural economy, households cannot be competitive if they refuse to specialize. Given the limited technologies available to them (agriculture and nonagriculture), specialization will help maximize production in the light of economies of scale. As an example, a specific industry for microenterprise development (nonagriculture), specific crops requiring special farming systems (and technology) for agriculture, or even specialization of services offered in a diversifying economic environment, will continue to raise their competitive advantage in that area. Specialization will stimulate efficiency in rural production and possibly curtail certain factors of production (in the hope of attaining efficiency). Among the factors of production, labor is easily substituted through the choice of appropriate technology, resulting in the displacement of many rural workers. This phenomenon was observed in the rural Philippines, which has been experiencing rural-urban migration for the past two decades or so. A sizeable proportion of labor migration spills over to other countries. In the desire for market efficiency, specialization can actually lead towards inequality because of the unequal utility values placed on different production activities. As Lewis (1984) points out, market efficiency is not the way to reach equilibrium in an agrarian economy; rather, it trades some social costs for gains in trade to serve as an engine of growth. The solution proposed then is empowerment of rural communities. Empowerment can include, but is not limited to, the provision of infrastructure and capacity building. The framework that this study will be based upon revolves around the complementation of infrastructure and capacity building in forging a path towards rural development.
The initial role of the government is neither regulation nor governance but empowerment of local communities, similar to the paradigm proposed by the World Bank in poverty alleviation. Empowerment is defined in this paradigm as "the expansion of assets and capabilities of poor people to participate in, negotiate with, influence, control, and hold accountable institutions that affect their lives" (Narayan, 2002, pp. 13–14). Focusing on empowerment in the framework, market efficiencies can be gradually attained since this will help in narrowing the information asymmetries among the stakeholders (the suppliers, the traders, the market/retailers, and the producers/farmers). The empowered stakeholders would like to gain access to pertinent information before they make specific decisions. Rural roads, other rural infrastructure, and capacitybuilding activities will enable all the stakeholders to access relevant information of the supply-demand chains for rural/agricultural goods and services. The stakeholders can use such information in the efficient allocation of factors of production.
In the process, the government needs to facilitate the dynamics where the stakeholders interact towards attainment of efficiency. For certain interventions like credit, direct provision of say seed capital may be provided by the government or can be taken from some other forms of development assistance. This is also true for other infrastructure where the initial construction will need money that is beyond the capability of the stakeholders. It is important though to consider that rural infrastructure does not follow similar protocol as in mainstream public economics where cost and maintenance will have to be secured from the beneficiaries through the process of taxation. Many of the rural beneficiaries in developing countries fall short of the cut-off of taxable income brackets. However, direct provision should not be continuously done; the government and donors will have to veer away from direct provision and focus on facilitation to stimulate the participatory environment leading towards sustainability. It is important for the stakeholders to establish ownership, so it is important to encourage them to contribute (in cash or in kind) in maintenance to safeguard the sustainability plan that should be part of the design of the intervention. The notion of a user's fee is difficult to inculcate among the stakeholders especially because they have limited income and livelihood opportunities. A good advocacy strategy though will help rural stakeholders and they will eventually accept the concept of user's fee.
In Section 4.5, models will be developed to understand the dynamics in the rural economy. A model for a household that would like to maximize its welfare function will be formulated taking into consideration spatial dimension. The spatial dimension will rationalize site-specific packaging of bundles of intervention. A stochastic frontier model (basically a production frontier) will also be developed with spatial dimensions. The spatial dimension is justified in terms of soil fertility and diversity of economic activities determined by topography, among others. This model will help explain how inequality among the rural households can be traced to how efficient/inefficient they are in accessing the factors of production available to them.
4.1 ROLE OF RURAL ROADS
A rural road will be defined as an access from the main road network to the rural communities and/or production areas. It is intended to provide an access path for individuals residing in rural communities and as passage for light public vehicles carrying people and/or produce. Transportation cost can be reduced because vehicles carrying farm loads will be cheaper than the human carriers that are still used whenever there is no such road, as in many rural areas of the Philippines.
Farm roads are often constructed as dirt pavement, or are topped with gravel, asphalt, or very seldom, concrete. Usually, only people and light vehicles pass through, but during harvest season, the local government or some community organization may upgrade it so that haulers can reach as close as possible to the production areas. The main road network, called national roads in the Philippines, are usually constructed with concrete materials and are wider. Thus, they accommodate heavy-duty haulers that will collect the produce and bring them to the main distribution depot (which is government or privately owned).
The path of rural development from the improvement of accessibility in the rural communities will start from the known direct impact of rural roads. Roads are intended to mitigate the state of isolation of an area isolation that is a hindrance to the initiation of various facets of development. Improved access roads among the rural households will bring increased accessibility and movement because of lower transportation costs, increasing economic activities. The literature provide a wide range of percentage reduction in transportation cost as a result of putting up new or improving existing rural roads. Regardless of the amount of input infused, rural roads are expected to contribute to lowering transportation cost.
Improvement in road networks starts up the feedback system of input procurement and marketing of produce. The producers are expected to pay less for the inputs of production because of the improvement in accessibility; this lower cost increases the producers' capability to procure more inputs. The different suppliers of inputs will lose their existing monopolies and be forced to become competitive because the farmers will have alternative sources. Marketing will no longer be limited to a few traders; a negotiable pricing system will be created because transportation cost reduction will open the ceiling of price negotiations. This is of course based on the assumption that commodity financing (usually associated with price ceiling of goods and being unfair to farmers) is no longer practiced or that there is a sustainable credit facility in place. Knowledge of the marketing avenues and the demand for various commodities (to be facilitated by the government) will encourage farmers' diversification of crops and later on, to their specializing in high valued crops that are viable only in the production area (efficiency). Thus, increased production and increased gross value coupled with lower input cost will benefit the farmers in terms of increased earnings.
Improved accessibility will also facilitate provision of basic social services like education and health. Even if such services are not brought right into the community, it will be easier for the households to access those from the town centers or in another community. Social services should result in enhancement of human capital and along with other capacity-building interventions, should contribute to empowering the rural community.
Rural roads will also generate multiplier effects. Foremost, they serve as a catalyst for greater public investment into infrastructure and capacity building. An improved access road will facilitate the construction of a health center (and visits of health professionals), a warehouse for agricultural commodities, and even the conducting of trainings and other capacity-building activities. Provision of other physical infrastructure will be made feasible with easy transport of materials. Then for those positions manned by personnel from outside the community, or for capacity building where resource persons come from outside, traveling into the community will be viable and less time will be spent in transit to the site.
The improved mobility of the households will expose them to outside communities. In this exposure, they may observe prototype development that will serve as a stimulus for their desire to realize similar development in their locality. This desire will then foster a good motivating factor for them to participate in the process of identification of strategies that can lead towards development. This is the start of community building that will later on evolve into a sustainable backbone.
With the growing demand for infrastructure, demand for support services will also increase, requiring more participation on the part of the household in planning and in sourcing for infrastructure and support services. This will stimulate the local government to contribute specifically for sustainability of the infrastructure and support services.
Improved accessibility among farmers (leading to reduction in transportation cost) brings viable input sourcing at reasonable cost. Furthermore, better post-production handling will result in lower post-production losses, yielding a good profit margin for the farmers.
For the non-agricultural household, the direct impact of roads will be in terms of facilitating the emergence of new investments and new enterprises. Eventually, there will be greater diversity in the livelihoods available to them. This diversity is an important manifestation of rural development.
The complementation between increased production among farming households and the non-farming households engaged in microenterprise development are early leads towards rural development. In rural areas where employment opportunities should extend beyond the traditional agriculture basis, the empowered households that participate in programs will benefit not just the individual households, but will strengthen the entire community as well, contributing to sustainability.
Rural development results from the improvement of the economic, social, and environmental conditions of the community. These three aspects complement each other and lead towards the overall improvement of individual and community well being.
The rural development and living condition scale and data used in this study come from (NEDA-WB-ASEM, 2005). A Likert scale is used to assess the perception of rural households on the different aspects of living conditions, including 18 items distributed among the different facets of living conditions. The scale was adopted from NEDA-WB (2003), which pilot-tested, validated and improved the instrument. Another Likert scale was also used to assess the perception of rural stakeholders on the different aspects of rural development, including 13 items distributed among the different constructs of rural development. In addition to the validation done in NEDA-WB (2003), the scale was validated further in NEDA-WB-ASEM (2005) to ensure data quality. The details of data collection strategies are given in Section 4.4.1.
4.3 IMPACT ASSESSMENT AND PERCEPTIONS
Impact assessment, participation, and perceptions have become integral elements in strategic development planning. Assessing the impact of similar past interventions can provide valuable lessons on what is effective and what is not, so that the mistakes of the past will not be repeated. Participation and involvement of beneficiaries ensures that the intervention planned to be implemented matches their needs. Perceptions provide a quick yardstick for development planners on the possible/potential impact of an intervention. This proximate measure is a fast alternative to waiting for the quantitatively measurable indicators of rural development, which usually manifest after a mid- to longterm period. Because the beneficiaries are the ones who will receive the outcomes, it is only appropriate that planners incorporate their perceptions into the plans of intervention. Participation and social preparation have become integral pre- and post-activities of rural development intervention strategies.
Here is a statement that further contributes to issues of participation and perception: the views of the stakeholders are considered valuable insights on the accomplishments of interventions of programs implemented, especially in rural areas (NEDA-WB-ASEM, 2005). While international comparability is easily guaranteed among assessments based on numerical yardsticks, the utility of such measures in the development of strategies for targeted interventions is limiting. Furthermore, participatory assessment has been considered as part of the poverty reduction strategy programs (PRSP) in many developing countries. The development of subsequent interventions (follow through) should be tailored to the stakeholder needs following their perceptions on what is effective for them. This could guarantee the acceptability of strategies and mechanisms of intervention in a much shorter time period, ensuring sustainability of the initial gains that may have been achieved by the predecessor project, parallel to the success of development projects that are backed with ample social preparations. Resource and public economics has similarly gained benefits from using contingent valuation methods that basically derive information from the perceptions by stakeholders in imputing prices and costs of non-traded goods and services.
The literature also includes the work of various authors on modelling with inputs from data on beneficiaries' perception. As an example, Prokopy (2005) measured outcome in terms of household satisfaction, equity in access, and saved time (from water collection) in a water system project. The thrust of decentralization was argued by Asthana (2003) as an element of participation, that public services provided by those closer to the people are more appealing. "Participatory" econometric modeling was done by Rao and Ibanez (2005) for a social fund in Jamaica; they concluded that although the funds do not necessarily address the perceived needs of the stakeholders, towards project completion, satisfaction of outcomes increases. This is especially true among social funds because it is expected that social order must be restored before economic gains will manifest. Participation was further pushed by DasGupta, et. al (2004), who emphasized the diversity of settings in the attainment of institutional changes, therefore requiring the tailoring of interventions to the needs/demand of beneficiaries.
4.4 DATA SOURCES
Data coming from two surveys will be used in the empirical investigation of the models presented below. The client satisfaction survey is one time point (crosssectional) data collected in 2005 where the unit of analysis is the household. The Family Income and Expenditure Surveys (FIES) have households as the unit of analysis. Public use files (PUF) of these surveys are available for 1985, 1988, 1991, 1994, 1997, 2000, and 2003, but concepts and sampling design have evolved over the years. The design and domain in 2003 are different from those of the previous years. Thus, only the crosssection for 2003 will be used in the analysis.
4.4.1 Client Satisfaction Survey
The Client Satisfaction Survey was commissioned by the World Bank in 2005 (NEDA-WB-ASEM, 2005) to develop a perception-based survey that will facilitate the verification of the effect of the outputs of the rural sector agencies (Department of Agriculture, Department of Agrarian Reform, and Department of Environment and Natural Resources) on rural development in the Philippines. A rural development and living condition scale (see Appendix 1) was developed and pilot-tested several times [see (NEDA-WB-ASEM, 2005) and (NEDA-WB, 2003)]. It was concluded that the scale can approximate the constructs of rural development. The survey was implemented in purposively selected barangays (villages) where households were then randomly selected. In the purposive selection of the barangays, prototype interventions of the departments were considered, along with an appropriate control group (no known intervention from the government in recent years). For the government interventions, the strata were defined in terms of whether the project was locally or foreign funded for each of the three major departments working in the rural sector (agriculture, agrarian reform, and environment and natural resources). The delineation between local and foreign funding serves as a proximate indicator of the intensity of resources used in implementing the project, where resources from local sources are usually lesser than those coming from foreign sources. The control group was also distributed according to expected income level (low, medium, high income), by topography (upland, coastal areas), and according to the Kalaban Laban Sa Kahirapan-Comprehensive Integrated Delivery of Social Service (KALAHI-CIDSS) sites (a government project using an integrated strategy of facilitating rather than direct provisions; it uses a participatory approach rather than imposing appropriate interventions). More than 6,000 households were included in the database. Only rural barangays were included.
4.4.2 Family Income and Expenditure Survey
The Family Income and Expenditures Survey (FIES) is conducted every three years by the Philippine National Statistics Office (PNSO). It is a probability sample of about 20,000 households with rural-urban areas of the provinces as domains (until 2000). In 2003, the domain was raised to the regions and sample size raised to 42,000. More detailed information was collected. This survey's unit of analysis is also the households, but in contrast to the information from the Client Satisfaction Survey, long-term outcomes are collected. Transportation cost is used as a proxy indicator of road system improvement.
4.5 HOUSEHOLD MODEL
Consider a household utility function where profit is indicated by realized or perceived rural development constructs. For perception on rural development constructs, two approaches will be considered: a dichotomous (presence-absence of rural development) one and an index developed from the rural development scale.
In a universal, unregulated intervention, those with more resources (e.g., land or education) will benefit more. This is called leakage of intervention in poverty alleviation strategies, where some intended beneficiaries were not reached while those who do not technically need the intervention actually benefited. In rural communities, such a leakage is very likely to occur especially when the marginalized sectors are still in the empowerment process. As an example, consider a capacity-building program such as livelihood training. Those who have higher education will have a good chance of appreciating the training and have the capability to apply it. They are also likely to have money for capital or may have easier access to credit. Unless a complementing credit program is offered, the more affluent will do better but the marginalized will remain marginalized, the income gap will expand, and the program will result in increased inequality among the rural households. This is also true even within the farming segment. In an irrigation project, the farmers would usually queue for their farm to get irrigation water. A farmer whose cultivated area is large will practically take most of the service time of the irrigation because he needs it. This may also result in greater inequality because by the time the small farmers access the service their paddies are already dried up, leaving them with damaged crops and an even lower income.
Given the natural conditions in a rural economy and the enhancements introduced by the development assistance (infrastructure and support services), the households want to optimize their benefits. The household dynamics aim to optimize their benefits resulting in improvement of their well-being. Such dynamics are summarized into a utility function defined as follows:
For the ith household, define
assuming linear contribution of the factors, for a household with farming activity,
Similarly, for a household with non-farming activity,
For the ith household, the total odds of having perceived that there is rural development is where The boundary conditions pertain to the exclusivity of household activities, if the household is engaged in non-farming activities only, and if the household is engaged in farming activities only.
The total income is Yi = Xi + Zi , determined by (assuming linear effect) or for farm income, and or for non-farm income. The last term of the models for income accounts for spatial dependence; a simple indicator is average income for the whole community in which the household is located.
Consider a measure of inequality P = Pq (y1, y2,...,yn) where n = total number of households and q = number of households with income below the poverty/food threshold. Some examples of P include the Gini coefficient, where yi is the income of ith household, or the Foster-Greer-Thorbecke Index (Foster et. al., 1984) given by , where yi = per capita income, z = poverty line, gi = z-yi called the poverty shortfall, q = number of poor households, and n = total number of families. Constraint in the model can be specified in terms of a target on the level of a measure of inequality.
The objective of a utility-maximizing household is to maximize given the total income Yi = Xi + Zi and the inequality-averse constraint P0 = Pq (Y1, Y2, ..., Yn) where P0 is some targeted poverty level. The constraint can be used so that funds intended for poverty alleviation will not be siphoned away by the segment above the threshold z from the marginalized segment in the process of maximizing their utility function. The constraint is attained when non-farm income increases while farm income is low. Both the expansion in farm and non-farm incomes can be realized whenever the intervention package is bundled so that the pre-requisite factors of farm production and skills and capital for non-farm income generation can be efficiently utilized. A household that may opt to concentrate on farm production can produce optimally (as supported by the interventions). This is also true for a household that has the skills to generate nonfarm income. All households are expected to expand income and other utility benefits, hence reducing income disparity.
The first–order conditions for optimality of the utility function can be derived by forming the Lagrangian function L(.), and subsequent optimization.
4.5.1 "Non-Poor" Households
The non-poor here are those households with income larger than the threshold z. Among this segment of the population, the inequality-averse constraint will not take effect in utility optimization if FGT is used. In FGT, only the income of the "poor" segment is included in the computation.
Contribution of Participation
The first-order condition for optimality of utility subject to the constraint and identity equation is .
The condition can be satisfied in two cases: (i) participation affects neither utility nor income from both farming and non-farming sources or (ii) participation affects utility and income function in opposite directions. Case 1 is easily satisfied if intervention is still in the early stage of community building. The stakeholders may not yet be able to realize the effect of participation on their utility or on their income. In case 2, utility will most likely benefit positively from participation, being a common objective/target in any community building activity. While they perceive better utility, participation may result in lower income initially because stakeholders allocate less time for their production activities, or because they allot a portion of earnings for the maintenance of the infrastructure. However, this is not expected to hold in the long-term. As participation becomes prevalent in that community, a model shift will occur or the effect of participation will longer be distinguishable because everybody will be participating.
Contribution of Availability of the Needed Intervention
For the infrastructure/intervention perceived to be available and needed in the community (I1i ), the first-order condition is . To satisfy the condition, there are also two cases: (i) farming and non-farming factors exceeded the threshold or (ii) farming and non-farming factors do not exceed the threshold. In case 1, access to the infrastructure/intervention will push income to grow but will not necessarily be accompanied by utility improvement. This is the case where the household has enough resources on hand, and will have greater expectations. Thus, although the infrastructure or intervention may indeed contribute to income growth, the odds of households perceiving rural development will not necessarily increase. In case 2, however, since the available resources to them (inputs of production) are still below the threshold, having perceived availability of an infrastructure/intervention that is needed will contribute not only to increasing the odds of perceived rural development, but the infrastructure or intervention effect will also manifest in terms of actual income growth.
Contribution of Mismatched Intervention
The effect of I2i and I3i will be similar, both having negative contributions in the utility function and having no contribution in the income functions. Considering I2i, the firstorder condition is . Perceptions such as those associated in I2i or I3i will be optimal if (i) the farming input is less than the threshold and non-farming input exceeds the threshold or (ii) the farming input exceeds the threshold and non-farming input is less than the threshold. In both cases, the seemingly unimportant I2i will have to impact positively if the household resources are still below the threshold (in either farming or non-farming inputs).
4.5.2 "Poor" Households
The poor households are those with income lower than the threshold z. For this segment of the population, the inequality-averse constraint contributes to utility optimization using FGT.
Contribution of Participation
The first-order condition is
This is satisfied when neither utility nor income is affected by participation. Thus, the poor are expected to manifest neither income nor utility improvement as a result of participation. Unlike the non-poor who may already exhibit growth in utility perception, the poor are expected to have income decline as a result of the time and money lost due to participation. That rate of deceleration in income should not pull away the low-income households from the threshold (z); otherwise, the objective function will not be optimized. A more intensive advocacy campaign will be needed so that the poor will able to appreciate the effect of participation later, and will not focus only on the immediate (unfavorable) consequence.
Contribution of Availability of the Needed Intervention
For the infrastructure/intervention perceived to be present and needed in the community ( I1i ), the first-order condition among the poor households is .
The poor households will most likely have farming and non-farming resources that are lower than the corresponding threshold. The optimal solution then implies that such needed intervention perceived to be available contributes directly to income increase (both farm and non-farm). In this case, agricultural infrastructure like rural roads, irrigation, post-harvest facilities, and even capacity-building activities will have direct contributions. On the other hand, the non-farming amenities would also include roads primarily, since they can stimulate trade and hence the growth of new economic activities leading to the expansion of rural livelihood. Livelihood training programs, credit, and microenterprise development will also have direct effects on non-farm income increase. Therefore among the poor households, the intervention to be implemented should be carefully chosen so that it will have direct benefit to them, and the utility function will be optimized effectively. Participatory project identification will help in this case.
Contribution of Mismatched Intervention
The same effect of mismatched intervention as in the non-poor described in Section 4.5.1 is expected among the poor households.
4.5.3 Other Implications
The perceived need and availability for rural infrastructure and other interventions yield varying effects for the groups above and below a specific income threshold. For the non-poor, access to infrastructure will increase perceptions of income but not necessarily of utility, as they may already have higher expectations. The poor, on the other hand, will benefit in terms of perceived utility improvement that is not necessarily associated with income increase.
To prevent further income disparities among the rural households, the views of the poor on the kind of project should be weighted more than those of the non-poor, who will generally benefit more. To help maximize utility and minimize income disparities, infrastructure or interventions should be chosen so that they will have direct immediate impact on the poor.
Those with lower production capacities should be able to access non-farm sources like participation in trainings or road access in order to avert inequality in income and maximize their utility. This can be done through a screening process for participants of trainings and application of a user's fee based on the ability to pay for physical infrastructure. Households that are assessed as being capable of paying will have less incentive to avail infrastructure, say, irrigation service. They will then procure their own irrigation, say an underground water irrigation type, therefore allowing more marginal households access to the irrigation system. The intervention would thus settle among the targeted beneficiaries. On the assumption that the local government unit is really concerned about the services they will deliver, they will also have a utility function that can be maximized when the households are satisfied with services, i.e., when the trainings/infrastructure becomes "sustainable."
Among agrarian reform communities, those who are efficiently collecting user's fees are more developed. Even in some social fund recipient areas in the Southern Philippines, road user's fees are collected using methods similar to economic rent for natural resources. Regular nonpayment of user's fees, for example irrigation dues, will result in curtailment of their privilege for their farm to be irrigated. Anything free is always viewed to be beneficial. Credit has always been perceived to be a dole out strategy. However, there is already a growing realization among the stakeholders that there is no such thing as a free lunch. There is an emerging paradigm shift from direct provision (favorable to politicians) to facilitation (sustainable) of access to various development amenities. When the role of the national government gradually shifts towards facilitation, the only way to sustain the project is to let the stakeholders participate in the maintenance (in cash or in kind). Such participation stimulates their sense of ownership of the infrastructure, hence increasing the prospects of sustainability.
The constraint then should not be imposed on utility maximization, but rather in the maintenance and sustainability of the intervention. For infrastructure, a user's fee system can be used not only to generate resources for maintenance, but also as an instrument in averting inequality (or at least to prevent it from further worsening). The user's fee system shall consider three factors: (i) capacity to pay this will help curb inequality, as the "better off" will contribute more than the marginalized group; (ii) economic rent it is fair that those who benefit more from an infrastructure will contribute more for its maintenance; and (iii) willingness-to-pay this should be considered because the user's fee might become a disincentive to use among some beneficiaries. Willingness-to-pay is easily encouraged through an effective advocacy campaign.
The constraint for inequality does not directly impact the utility-maximizing households. It is natural behavior that when development intervention in any form is available, rural households will take advantage of whatever benefit it may yield. Hymer and Resnik (1969) pointed out that inequality in an agrarian economy can worsen because of the increasing trade with the outside economy becoming more beneficial to a certain "advantageous" segment and detrimental to the marginal sector.
The model has several variables and a good number are dichotomous (dummy) variables. Estimation using least squares may be affected because the design-matrix can become ill-conditioned. Estimates may yield reverse signs, so sensitivity analysis on each independent variable may not be feasible. Forecasting/prediction may still be viable, however, even when the least squares method is used in the presence of ill-conditioning in the design matrix.
To resolve the potential problem caused by ill-conditioning in the design matrix, the backfitting algorithm is used in the estimation. The algorithm assumes that the postulated model is additive, a generalization of the linear regression model. The model is expressed as a sum of basic functions that can be linear, non-linear, or non-parametric. The additive model is given by
(ii) Cycle: j = 1,2,...,r
Continue (ii) until the individual functions do not change where Sj denotes a smoothing of the response y against the predictor xj. Smoothing may reduce to ordinary least square for simple regressions (one-at-atime) if the functions are linear.
4.5.5 Specification of Variables
The response variables are total income and the rural development index (standardized so that values range from 0 to 100). The total income coincides with farm income if the household derives all income from farming, non-farm income if it earns income from non-farm sources, and the aggregate of farm and non-farm income if it derives income from both sources.
The survey design imposes constraints in the choice of inputs of production (farming) among the households. Some proximate indicators were considered in lieu of real production inputs so that the production function becomes comprehensive. This will provide a rationale for the estimates of technical efficiency. The following inputs of production will be considered: area cultivated, access to irrigation, access to and utilization of credit (as proximate indicators of procurement of farm inputs or capital availability for non-farm activities, a requirement for the development of small-scale industries), whether single or multiple crops are planted (proximate indicator of farming system), health indicator of household members (as proximate indicator of human capital), number of household members with work (non-farm), and tenure of work. Two dummy variables will also be included:
If the household derived income from both farming and non-farming sources, then S1 = S2 = 1. The interaction between S1 and farming inputs, and S2 with non-farming inputs will be included to ensure that causation between output and production inputs are appropriate.
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