Agricultural efficiency and welfare in South Africa

Abstract

Agricultural and food commodity price declines associated with domestic and international agricultural efficiency gains can have important welfare effects for a country. While food price reductions benefit low-income consumers in particular, they may also cause declines in agricultural employment, leading to some resistance to technological change as a policy goal. The simulations reported here use a South African Computable General Equilibrium model with highly disaggregated food and agricultural sectors to illustrate the various effects of such agricultural efficiency gains. The results suggest that technological advances in agriculture should not be resisted because of their negative impact on agricultural employment; the welfare gains from declining prices are too important, while employment gains in other (growing) sectors are likely to outweigh the loss of agricultural employment. In the face of increasing international efficiency South African agriculture should be encouraged to respond by also increasing its efficiency, despite the negative consequences for employment in the industry, as a failure to do so may be even more detrimental to the poor in terms of overall employment.

1. INTRODUCTION

Policymakers in developing countries often place a great deal of emphasis on the need for increased competitiveness and efficiency gains in domestic agricultural sectors. This is understandable given that agricultural exports are typically an important source of foreign revenue for developing countries. Efficiency gains are also associated with a reduction in food prices, which is an important contributor to the fight against poverty. However, at the same time the agricultural sector is frequently identified by the same policymakers as an important source of employment growth. There is a misconception that increased efficiency in an industry will necessarily lead to increased employment. In fact, the direct or first-round effect is the opposite, since efficiency gains allow producers to produce a unit of output using fewer inputs than before. However, increases in (real) incomes associated with efficiency often result in expansions of economic activity. Thus, if efficiency gains in an industry are coupled with increased production levels overall, the associated indirect increases in employment may actually be greater than the direct reduction in employment. This process is complicated by international trade; unless domestic efficiency gains at least ‘equal’ international efficiency gains an economy is likely to lose competitiveness, and hence even where there are absolute gains in domestic efficiency there may be a loss of employment.

This presents an important policy challenge. While efficiency gains are imperative from a competitiveness point of view, there has to be a realisation that the agricultural sector is a declining one and unlikely to remain an important source of employment: this is part of the natural development path of any (developing) country. Arguably a government should recognise the nature of this transition and play a role that facilitates the transition process from an agrarian society to an industrial one through training and support policies that reduce the costs of transition.

In this paper the various positive and negative welfare effects of domestic and international agricultural efficiency gains are analysed within a South African context in order to illustrate some of the arguments above. Advances in microeconomic theory and empirical methods have enabled researchers to simulate and evaluate the impact of economic shocks with economy-wide effects. In particular, estimates of the socio-economic impacts of domestic and international efficiency changes are generated with a computable general equilibrium (CGE) model for South Africa, calibrated with a social accounting matrix (SAM) with highly disaggregated food and agricultural sectors.

2. TECHNICAL CHANGE

2.1 Theoretical underpinnings

Consider a simple linearly homogeneous production function with two inputs, capital (K) and labour (L) with constant returns to scale defined by

Total factor productivity (TFP) growth (also referred to as technical change or efficiency gains) can be defined as the rate of change of the technology (A) used in the production process. Efficiency gains thus affect the relationship between inputs and output by enabling producers to produce a unit of output using fewer inputs than before.

In a competitive market environment the benefits of efficiency gains are typically realised as reductions in real commodity prices, and hence also an increase in output (ceteris paribus). In order to distinguish between the impacts of technical change on output growth from the impacts of changes in input use on output growth, Robert Solow's ‘growth accounting’ method can be used. The total differential of the production function identifies the change in output (dQ) for changes in labour (dL), capital (dK) and technology (dA), which on dividing through by output (Q), to give the percentage change in output, and reorganising, yields

MP _K and MP _L are respectively the marginal products of capital and labour.

If the production function is characterised by constant returns to scale the expressions in brackets, which identify each factor's share of total output, sum to one (Euler's Theorem). Therefore technical progress is defined as the growth in output unexplained by the growth in inputs, i.e.,

Growth accounting was initially designed for application in economy-wide production functions. However, it is often used to analyse industry-level TFP changes. In practical applications industry-level production functions typically include not only primary factors of production, but also intermediate inputs. If measured correctly, industry-level TFP growth should reflect the increase in efficiency originating from within an industry, i.e. excluding reductions in unit costs attributable to TFP growth in other industries that supply intermediate inputs. For example, greater efficiency in agricultural production will cause agricultural commodities to become cheaper and hence food processing industries benefit indirectly. Although this is an important consideration when analysing industry-level TFP growth rates using historical data, it is less of a concern when simulating the impact of industry-level TFP growth rates, as is done in this paper (see Domar, 1961; McDonald, 1992 for some further insight in this regard).

The employment implications of technical progress have multiple determinants. If output growth is greater than aggregate input growth then aggregate factor employment will increase, if not then aggregate employment of factors will decline. Where domestic demand for a commodity is income inelastic, which is typically the case for agricultural and food commodities, it is likely that aggregate factor employment will decline, unless the increase in export demand is sufficiently large to produce an overall increase in demand. In the presence of factor biased technical progress the impacts on the use of specific factors are less clear-cut; typically factor-saving technical progress will reduce employment of that factor but it may generate increases in the employment of other factors. Moreover, when technical progress in agriculture is land-saving this is more likely to produce increases in the employment of other factors, despite the impact of effects associated with Engels ‘Law’, because land is typically a fixed factor.

For each activity (or industry) included in the CGE model a unique two-tier production structure is specified that allows for the analysis of various different types of technical change. At the top level of the production structure (see Figure 1) aggregate primary inputs (or value added, denoted by QVA) and aggregate intermediate inputs (QINT) are combined in a constant elasticity of substitution (CES) function to form final output (QX). At the second level, primary inputs (F ₁, F ₂,…, F _n ) are combined in a CES production function to form QVA, while various commodities (C ₁, C ₂,…, C _n ) used as intermediate inputs are combined in a Leontief function to form ‘aggregate’ intermediate input, QINT.

Figure 1. Two-tier production structure

Algebraically, the value added production function

is embedded in the top-level CES production function

where the parameters A _QX and A _QVA serve as ‘efficiency parameters’. The sigma terms (σ _QVA and σ _QX ) represent the elasticities of substitution for each of the functions. Given these formulations, technical change can now be defined in a variety of ways. First, it can be an improvement in the way value added (QVA) and intermediate inputs (QINT) are combined in the top-level production process, captured in the CGE model as an increase in A _QX . In this formulation the productivity levels of both primary factors and intermediate inputs are increased by the same proportion.

Second, technical change can be an improvement in the efficiency at the second-level value added function, representing an increase in the efficiency with which all factors are used, and captured as an increase in A _QVA . This results in a biased form of technical change at the level of the production of QX, in the sense that producers will use more primary factors relative to intermediate inputs due to the relative improvement in their productivity.

A third type of technical change, factor biased technical progress, can be implemented in the model as a change in the productivity of a specific primary factor, ¹ say F _k , for example, soil erosion caused by poor agronomic practices may cause the flow of productive services from a given area of land to decline. Finally, there may be a combined effect whereby efficiency changes occur at the top level and/or at the second level and/or within one of the primary factors of production. ²

Efficiency changes in competing foreign industries can also have important effects on the domestic economy, especially for a small, open economy that acts as a price taker in world markets. Efficiency changes in foreign industries have a direct impact on the domestic economy via changes in world prices of imports and exports. Consequently, in the CGE model, international efficiency gains are captured as reductions in the world prices of imports and exports.

2.2 Technical change in South African agriculture

Although the South African agricultural sector has not performed particularly well during the last four decades, as measured in terms of gross value of output, there is, at least, evidence that the volume of output has not declined during the last decade. Consequently the decline in the gross value of agricultural production can be attributed to declining commodity prices (Vink, 2000). This warrants further investigation into productivity changes in the agricultural sector as a possible source of these price declines. Hartzenberg and Stuart (2002) find that the agricultural sector was one of only a few sectors that experienced positive TFP growth over all the time periods examined (see Table 1), while Vink (2000) and Thirtle et al. (2000) find evidence of a recovery in agricultural TFP growth during the 1990s.

Table 1: TFP growth estimates for South Africa (1960–1999) (percentage change)

(Vink, 2000)		(Thirtle et al., 2000)		(Hartzenberg & Stuart, 2002)
Period	TFP growth (agriculture)	Period	TFP growth (agriculture)	Period	TFP growth (agriculture)	TFP growth (total)
1960–1980	2.05	1965–1981	2.15	1960–1976	1.00	–1.00
1980–1990	0.96	1981–1991	2.88	1976–1989	1.70	0.00
1980–1996	1.19
1990–1996	1.56			1990–1999	N/A	0.80
1960–1996	1.66
Note: Comparisons should be made with care since time periods, data sources and growth decomposition techniques may differ.

Many factors have contributed to the revival in agricultural productivity, most notably the cost–price squeeze experienced by agricultural producers (Vink, 2000). This was caused by a range of factors, including the depreciation of the domestic currency, increased labour market costs and lower levels of trade protection. As expected, agricultural employment levels have declined fairly rapidly as a result of, among other things, increased efficiency, which has enabled farmers to mitigate the impact of the cost–price squeeze on farm incomes (Van Zyl et al., 1993). Productivity growth is likely to continue given the increased openness of world trade and advances in production techniques, and hence further job losses are to be expected.

3. Computable General Equilibrium Model and Data

3.1 CGE model

The PROVIDE Project CGE model is used to assess the impact of domestic and international production efficiency changes. This model is a member of the class of single country CGE models that are descendants of the approach to CGE modelling described by Dervis et al. (1982). The model adopts the SAM approach to modelling (see Pyatt, 1998). The SAM serves to identify the agents in the economy while quantifying the transactions between various agents in the economy. A detailed description of the model's behavioural relationships can be found in PROVIDE (2005a). The production structure used in the model has been briefly described in section 2.1.

The SAM used to calibrate the model contains a large number of factor (labour) and household accounts, thus supplying rich information about the patterns of employment and the functional distribution of income. The CGE model uses these data to generate, in the present context, detailed analyses of the distributional implications of the changes in efficiency. Consequently the implications for the patterns of South African trade are regarded as being of secondary importance, and therefore the analyses below focus on aggregate trade patterns. ³

3.2 Social accounting matrix

The SAM is a 309 account aggregation of the PROVIDE Project SAM for South Africa in 2000. The model SAM has 32 commodity (or product) groups (of which 3 are agricultural and 11 are food commodities) and 39 activity (or producer) groups (of which 9 are agricultural and 11 are food activities).

The SAM used in this model further includes 56 factor groups (54 labour groups disaggregated by province, race and skill levels, and capital and land), and miscellaneous enterprise, government, capital (savings and investment) and rest of the world accounts. In addition there are 162 household groups (distinguished by province, racial groups, location, gender and educational attainment of the head of the household). The combination of a large number of labour types and household groups supplies the institutional detail that allows the CGE model to capture the distributional implications of technical progress; a particularly important component of the institutional detail is the identification of factors and households by race and province, since, as the subsequent analyses demonstrate, these characteristics are relevant to the distribution of the gains from technical progress.

In the context of the SAM, ‘agricultural commodities’ refers to primary agricultural output produced by agricultural activities, and ‘food commodities’ refers to processed food products produced by food manufacturing industries that use, inter alia, primary agricultural outputs as intermediate inputs. Agricultural products and processed food products are therefore produced by various sectors of the economy using fundamentally different production technologies, but there exist close interdependencies between the two production sectors as they form part of the same value chain. A listing of the agricultural and food activity and commodity accounts appears in Table 2.

Table 2: Input and output patterns of agricultural and food industries

	Share of gross output (%)		Share of value added (%)			Output composition (%)
	Intermediate inputs	Value added	Capital	Land	Labour	Field crops	Horticulture	Livestock and other animals
Agricultural industries
Agriculture Western Cape	47.62	55.25	47.00	9.68	43.32	6.83	64.58	28.59
Agriculture Northern Cape	41.86	61.43	28.82	8.48	62.71	24.03	35.87	40.10
Agriculture North West	53.65	49.73	38.21	11.47	50.32	37.98	11.01	51.01
Agriculture Free State	58.70	45.23	54.04	14.33	31.64	41.13	14.18	44.68
Agriculture East Cape	46.29	57.67	33.30	9.53	57.17	5.06	31.58	63.36
Agriculture KwaZulu-Natal	48.03	55.48	33.36	10.08	56.56	33.08	16.61	50.32
Agriculture Mpumalanga	55.45	48.04	58.23	13.77	28.00	29.03	39.68	31.29
Agriculture Limpopo	48.09	55.06	41.50	7.45	51.05	12.64	64.05	23.31
Agriculture Gauteng	58.64	45.59	58.42	14.47	27.11	9.85	22.69	67.46
Agricultural industries (values – R million)	31 032	31 919	14 035	3456	14 427	13 179	21 331	24 267
Food industries
Meat	96.76	3.91	29.82		70.18
Fish	82.19	17.93	64.62		35.38
Fruit	83.01	17.62	48.04		51.96
Oil	88.00	12.81	60.10		39.90
Dairy	87.09	13.30	39.73		60.27
Grain mills	82.63	17.84	53.65		46.35
Animal feed	87.03	13.81	43.98		56.02
Bakeries	80.52	19.74	30.68		69.32
Sugar	85.59	14.79	80.41		19.59
Other food	74.74	25.76	56.52		43.48
Beverages and tobacco	73.42	25.91	66.56		33.44
Food industries (values – R million)	133 087	25 086	13 939		11 147
Other industries
Other industries	60.37	40.32	45.48		54.52
Other industries (values – R million)	1 125 878	751 921	341 998		409 923

A feature of the SAM that justifies emphasis here is the treatment of activities and specifically agricultural activities. Usually each activity in an input–output structure produces a single commodity and each commodity is produced by a single activity. The CGE model, however, is set up to allow for multi-product activities, and therefore the SAM uses a supply and use structure that allows for the possibility of multi-product activities. Agricultural activities are defined by reference to provinces of the country. Thus, each agricultural region can produce a range of commodities, and the profitability of farming for all agricultural activities depends upon the effects of policy shocks on these commodity (output) prices. A detailed description of the development and features of the SAM can be found in PROVIDE (2006).

3.3 Descriptive statistics

The descriptive statistics based on the SAM are, because of the focus of the analyses, limited to agriculture and food activities and commodities. In general about half of agricultural input costs are accounted for by primary inputs (value added), with the rest being accounted for by intermediate inputs and small production subsidies (see Table 2). However, across the provinces the shares of value added to broad factor types differ appreciably; the share to labour varies from a low of 27 per cent to a high of 63 per cent with some evidence of an inverse relationship between the shares of intermediates in gross output and the shares of labour in value added. There are, as a more detailed examination of the SAM confirms, substantial differences in the input structures of agricultural production across the provinces of South Africa. This is unsurprising given the substantial differences in the commodity output compositions that are reported in the final three columns of Table 2; these output composition shares also demonstrate the extent to which the commodities produced in agronomic regions across South Africa differ and hence the potential importance of a multi-product activity representation of production.

The production relationships for the food industries differ markedly from those for agriculture. Intermediate inputs account for overwhelming shares of production costs (73 to 97 per cent), with the rest being accounted for by value added, given the low rates of production subsidy. The shares of labour in value added are variable but not far out of line with the national average (55 per cent) (see Table 3).

Table 3: Consumption of agricultural and food products

	Share of total demand (%)		Share of final demand (%)
	Intermediate demand	Final demand	Household consumption	Exports
Agricultural products
Field crops	85	15	0	100
Horticulture	12	88	77	23
Livestock and other animals	55	45	88	12
Agricultural products (values – R million)	31 508	34 362	25 127	7592
Food products
Meat products	21	79	98	2
Processed fish products	9	91	82	18
Fruit and vegetable products	14	86	75	25
Oils and fats products	52	48	93	7
Dairy products	17	83	98	2
Grain mill products	29	71	97	3
Animal feeds	85	15	96	4
Bakery products	3	97	100	0.4
Sugar products	32	68	92	8
Other food products	35	65	90	10
Beverages and tobacco	25	75	88	12
Food products (values – R million)	43 232	122 976	113 027	8997
Other goods and services
Other goods and services	55	45	64	36
Other goods and services (values – R million)	1 215 255	981 651	433 849	240 004

A major reason for the high shares of intermediate inputs for the food industries is the dominance of raw agricultural commodities in the input cost structures of the food industries; this is reflected in the importance of intermediate inputs as a source of demand for agricultural commodities and the commensurately low shares of agricultural commodities sold to final demand. Note also how household consumption of agricultural and food commodities is dominated by food commodities, and similarly how food commodities are the primary source of exports. This indicates how important it is to include the food industries in analyses of agricultural activities.

4. Policy Analysis

4.1 Policy scenarios

A series of policy simulations explores the effect of domestic and international efficiency gains in agricultural production on the South African economy. The intention of these explorations is to provide insights into how developments in the South African agricultural sectors might contribute to the wider objectives of the South African government. These explorations are not driven by the immediate or imminent pressures of current policy questions but are rather inspired by the general argument that an understanding of how economic systems might react to changes in the production climate is an important input to the development of economic policies.

The scenarios reported focus on domestic technology changes within the agricultural industries. A series of simulations is also devoted to international technology changes that affect the domestic economy via their impact on world prices of agricultural and food products. Thus, three sets of simulations, named DOMSET, INTSET and COMSET, each containing five simulation loops, are reported on:

• DOMSET: Domestic agricultural efficiency gain at the top level of the production structure, i.e. where intermediate inputs and primary factors are combined. In simulations sim01 to sim05 efficiency is increased from 1 per cent to 5 per cent in 1 percentage point increments.

• INTSET: International agricultural efficiency implemented as a reduction in the world prices of imported (pwm) and exported (pwe) food and agricultural commodities. In simulations sim01 to sim05 the world prices of agricultural commodities are reduced by 1 per cent to 5 per cent in one percentage point increments, while at the same time the world prices of food commodities are reduced by between 0.5 per cent and 2.5 per cent (0.5 percentage point increments). The rationale here is that agricultural efficiency gains have a direct effect on agricultural commodity prices, and to a lesser extent on food commodity prices. The (optimistic) assumption is that international food prices will fall by half those of agricultural commodity prices.

• COMSET: A combination of sim04 in INTSET and the entire simulation range in DOMSET. This implies that the five simulations in COMSET (sim01 to sim05) model domestic agricultural efficiency increases of between 1 per cent and 5 per cent (as in DOMSET), while at the same time a 4 per cent reduction in the world price of agricultural commodities and a 2 per cent reduction in the world price of food commodities (sim04 in INTSET) is included in each simulation.

In all cases the simulations assume that the origins of these technological changes are exogenous, i.e. the model provides no explanation of how these changes originate nor does the model include allowances for the research and development costs of new technology.

4.2 Model closure rules

The model closure rules were selected with the objective of providing a realistic representation of the South African economy. Mathematically speaking, closure rules ensure that the numbers of variables and equations in the model are consistent, a necessary condition for the model to find a unique solution. In economic terms, closure rules define fundamental differences in perceptions of how economic systems operate. The PROVIDE CGE model allows for a wide range of alternative market clearing and macro-economic closure conditions; it is standard practice to assess the sensitivity of results to the choice of closure conditions by running the experiments with a range of closure options. The rules selected, and main variants used for sensitivity analyses, are discussed briefly below.

The foreign exchange market clears via a flexible exchange rate. South Africa as a small country is modelled as a price taker on international markets, i.e. foreign import and export prices are fixed. The capital account, which records all savings and investment-related transactions, is closed by assuming that the share of investment expenditure in total final domestic demand remains constant. The equilibrating variables are the savings rates of all households and incorporated business enterprises, which are allowed to vary equiproportionately. The government account is closed by variations in the level of government borrowing or savings – that is the budget deficit or surplus. All tax rates are assumed to remain constant, while government consumption is a fixed share of total final domestic demand. An alternative wherein government savings were fixed and the direct (income) tax rates on households and enterprises vary to clear the government account was implemented but had very little effect on the results (see below).

The factor market closure involves different treatments for different types of factors. Labour is categorised into three groups, namely (1) low-skilled and unskilled workers, (2) medium-skilled workers and (3) skilled and high-skilled workers. The medium-skilled and skilled/high-skilled groups are assumed to be fully employed and mobile across various sectors in the economy, and hence the equilibrating variable is the wage rate. In contrast, the supply of low-skilled/unskilled labour is assumed to be perfectly elastic, based on the assumption that there is excess capacity (unemployment) of this type of labour in the economy. Activities can increase the employment of unskilled workers so long as they are willing to pay the constant wage. Thus, any changes in demand for unskilled workers are reflected in changes in employment levels, while changes in demand for skilled workers are reflected in changes in wage rates. An alternative with the assumption that low-skilled and unskilled workers were fully employed was also implemented. Although this did affect the results (see below), the results with unemployed low-skilled and unskilled labour remain the focus since these are considered a more realistic assumption for this labour cohort.

For physical capital two scenarios are explored: a short-run scenario where the quantity of capital used by each activity is fixed, which means that the industry-specific return on capital adjusts, and a long-run scenario where capital is assumed to be mobile across sectors, thus moving to those areas in the economy where the return on capital is the highest. The discussion of the results focuses on the short-run scenario. The use of the factor land is fixed at the industry level, which reflects the fact that agricultural activities are defined by geographic location.

All prices in a CGE model are expressed relative to the numéraire, a fixed price (or price index) in the model. In this study the model numéraire is the consumer price index (CPI), and consequently all the value results of the model are expressed in real terms.

4.3 Results and analyses ⁴

4.3.1 Domestic efficiency gains (DOMSET)

Table 4 reports on various price and quantity changes arising from efficiency gains of 4 per cent in all agricultural industries (sim04). Based on the average agricultural TFP growth estimates for various periods shown in Table 1, 4 per cent represents the efficiency gains in agriculture that can be expected under normal circumstances over a period of one to two years, which is a relatively short time span, hence the concentration on the short-run scenario. As a result of the efficiency gains agricultural producers use fewer intermediate inputs (QINT) and value added (QVA) also declines. The greater efficiency allows a unit of output to be produced at a lower cost, and hence producer prices (PX) decline by around 4 per cent. The range of results for producer prices is a reflection of both the input and output mixes of agricultural activities in various areas of the country; the near inverse relationship between domestic production (QX) and producer prices is primarily driven by the differences in output mixes (see Table 2). These gains are passed on to consumers in the form of lower purchaser prices for agricultural commodities (PQD) (see Table 4); in particular, prices for field crops drop by 2.7 per cent, horticultural products by 4.0 per cent and livestock by 6.3 per cent. The drop in livestock prices reflects the importance of cost reductions via intermediate inputs and explains the decline in total output by the animal feeds activity.

Table 4: Changes in intermediate inputs, value added and domestic production for efficiency gains of 4 per cent in all agricultural industries (DOMSET, sim04, percentage changes)

	Intermediate inputs		Value added		Domestic production
Industries	Quantity (QINT)	Price (PINT)	Quantity (QVA)	Price (PVA)	Purchaser prices (PQD)	Prices (PX)	Commodity groups	Purchaser prices (PQD)	Domestic production (QXC)
Agricultural production regions in South Africa							Agricultural commodity groups
Eastern Cape	− 3.71	− 0.12	− 1.48	− 1.26	1.42	− 4.57	Field crops	− 2.67	2.87
Free State	− 1.81	− 0.14	− 0.33	− 0.88	2.79	− 4.29	Horticulture	− 4.02	3.17
Gauteng	− 2.63	− 0.59	− 0.59	− 1.62	2.19	− 4.85	Livestock & other	− 6.29	1.82
KwaZulu-Natal	− 1.70	− 0.06	− 0.73	− 0.55	2.77	− 4.16
Limpopo	− 0.41	− 0.01	− 0.28	− 0.07	3.65	− 3.88
Mpumalanga	− 0.72	− 0.07	− 0.19	− 0.34	3.50	− 4.03
Northern Cape	− 2.05	0.08	− 0.72	− 0.59	2.69	− 4.15
North West	− 2.21	− 0.26	− 0.85	− 0.94	2.38	− 4.41
Western Cape	− 0.69	− 0.02	− 0.28	− 0.23	3.51	− 3.97
Processed food industries							Processed food commodity groups
Animal feeds	− 1.48	− 0.79	− 1.35	− 0.86	− 1.46	− 0.80	Animal feeds	− 0.87	− 1.33
Bakeries	0.44	− 0.10	− 0.17	0.21	0.32	− 0.04	Bakery products	− 0.08	0.40
Beverages and tobacco	1.21	− 0.14	0.01	0.46	0.90	0.02	Beverages and tobacco	− 0.03	0.90
Dairy products	0.82	− 0.75	− 0.57	− 0.06	0.64	− 0.66	Dairy products	− 0.73	0.63
Fish products	0.85	− 0.25	− 0.06	0.21	0.69	− 0.17	Processed fish products	− 0.21	0.69
Fruit	1.00	− 0.19	− 0.02	0.31	0.83	− 0.11	Fruit and vegetable products	− 0.22	0.81
Grain mills	1.00	− 0.91	− 0.45	− 0.19	0.74	− 0.78	Grain mill products	− 0.82	0.74
Meat products	1.00	− 1.58	− 1.28	− 0.45	0.91	− 1.54	Meat products	− 1.63	0.91
Other food products	1.45	− 0.82	− 0.19	0.00	1.03	− 0.61	Other food products	− 0.61	1.02
Oils	1.66	− 0.62	− 0.06	0.23	1.44	− 0.52	Oils and fats products	− 0.30	1.42
Sugar	0.81	− 0.29	− 0.04	0.13	0.68	− 0.22	Sugar products	− 0.28	0.69

The greater efficiency in agriculture has a knock-on effect for food producers, who gain from lower prices of agricultural intermediate goods (PINT). Due to the change in relative prices of intermediate inputs and value added, producers change their input mix by using more intermediates (QINT) and less value added (QVA). Food production costs decline and in turn are passed on to consumers (lower PQD). These price reductions are substantially lower than the initial reductions in agricultural commodity prices, which reflects the fact that only about one-quarter of food producers' costs are accounted for by agricultural intermediates. Overall demand for food and agricultural commodities increases in response to lower prices, and hence producers generally increase production (QX). However, the increase in domestic production of agricultural commodities (QXC) is uniformly less than the increase in efficiency due to the effect of Engels Law; the relatively greater increases for horticulture and field crops are largely a consequence of increased export demand.

Table 5 shows the commodity flow (demand- and supply-side) effects for food and agricultural commodities. Note that the table reports percentage changes in quantities, not values. The 11.3 per cent surge in agricultural exports is evidence of agricultural producers' greater competitiveness vis-à-vis foreign producers. Lower domestic agricultural and food commodities prices also lead to an increase in domestic demand for domestically produced goods (QD). As a result domestic agricultural production (QXC) increases by about 2.2 per cent (on average) compared to 0.7 per cent for food production. A substitution effect is noticeable on the import side, with consumers substituting domestically produced goods for imported agricultural and food commodities (QM). There is also an income effect as reflected in the overall increase in the composite domestic commodity (imported and domestically produced goods) (QQ) by about 0.7 per cent for agricultural goods and 0.5 per cent for food commodities.

Table 5: Commodity flows for efficiency gains of 4 per cent in all agricultural industries (DOMSET, sim04, percentage changes)

	Domestic production (QXC)	Composite commodity (QQ)	Domestic demand (QD)	Exports (QE)	Imports (QM)
Agricultural commodities	2.22	0.73	1.08	11.31	− 4.85
Food commodities	0.74	0.53	0.65	2.10	− 1.14
Other commodities	0.11	0.18	0.16	− 0.24	0.32
Total	0.22	0.22	0.23	0.19	0.19
Note: The commodity (product) accounts in the SAM are disaggregated into various agricultural and food commodities. The percentage changes reported here are the percentage changes in the total quantities of agricultural and food commodities and thus represent a ‘weighted’ average percentage change.

Efficiency gains also affect factor demand (FD) (see Table 6). Since the marginal productivity of factors increases, fewer workers are needed to produce a unit of output. Despite the increase in output (QX) all agricultural producers reduce their demand for all factor groups. There is also a decrease in demand for labour in food-producing industries but, as explained previously, this is an indirect effect resulting from the changing relative prices of intermediate inputs and value added rather than a direct effect of the agricultural efficiency gains.

Table 6: Factor demand (FD) effects for efficiency gains of 4 per cent in all agricultural industries (DOMSET, sim04, percentage changes)

	Unskilled/unemployed		Medium-skilled/Fully employed			High-skilled/Fully employed
Factor groups	African	Coloured/Asian	African	Coloured/Asian	White	African	Coloured/Asian	White
FD (agric)	− 1.36	− 0.68	− 1.16	− 1.39	− 1.17	− 1.73	− 0.95	− 1.17
FD (food)	− 0.34	− 0.18	− 0.45	− 0.48	− 0.62	− 0.74	− 0.70	− 0.83
FD (other)	0.45	0.30	0.06	0.05	0.13	0.01	0.02	0.06
Total	0.28	0.19	0.00	0.00	0.00	0.00	0.00	0.00

Given the assumption that medium-skilled and high-skilled workers are fully employed and mobile between sectors, the skilled factors that are released from the agricultural and food industries are absorbed elsewhere (FD ‘other’) in the economy so the overall level of employment remains unchanged. However, the higher productivity of skilled workers means that their wages increase. The net effect is a higher factor income (YF) for all skilled workers (see Figure 2). Importantly, the results also show an increase in demand for unskilled labour in non-agricultural and food sectors due to increased overall economic activity (see Table 6). Consequently the net employment effect for unskilled workers in the economy is positive: African employment increases by about 0.3 per cent and Asian/coloured employment by 0.2 per cent. These increases are not substantial, but suggest that employment losses in agriculture and food sectors are more than made up for in other sectors. The total factor income of unskilled workers increases as a result, although generally the increase is not as high as for skilled workers (see Figure 2). As demonstrated in Figure 2, these results are not sensitive to the assumption of fixed government deficit, but the sizes of the factor income effects are marginally sensitive to the assumption of unemployed unskilled labour. ⁵

Figure 2. Economy-wide factor income effects (YF) for efficiency gains of 4 per cent in all agricultural industries (DOMSET, sim04, percentage changes)

There are a number of important qualifications to these results. First, the employment gains are only realised once all the general equilibrium effects have worked through the system. And, second, the results refer to groups of workers, not individuals. Those unskilled workers released by the agricultural sector are not necessarily the ones finding employment in the non-agricultural sectors. ⁶ It may therefore be that rural unemployment, associated with employment in the agricultural industry, increases, while urban unemployment, associated with other industries, decreases, with an overall net positive effect on the employment of unskilled workers.

4.3.2 International technical change (INTSET)

International agricultural efficiency gains are captured as a reduction in the world prices of agricultural and food commodity imports and exports. The food commodity prices are reduced by half that of agricultural commodity prices to account for the fact that food prices are likely to be less affected by agricultural efficiency gains than by agricultural commodity prices.

The commodity flow effects of sim04, which simulates a 4 per cent (2 per cent) reduction in world agricultural (food) commodity prices, are shown in Table 7. A reduction in the world price of exports (pwe), ceteris paribus, will cause domestic producers to shift output towards the domestic market (QD) and away from the export market (QE declines by 6.5 per cent and 3.7 per cent for agricultural and food commodities respectively). This causes the trade balance to deteriorate, leading to a depreciation of the nominal exchange rate. If at the same time there is also a reduction in the world price of imports (pwm), domestic demand for imports will rise (QM increases by 2.7 per cent and 2.4 per cent for agricultural and food commodities respectively), thus putting further pressure on the exchange rate to depreciate.

Table 7: Commodity flows for a 4 and 2 per cent reduction in world agricultural and food commodity prices respectively (INTSET, sim04, percentage changes)

	Domestic production (QXC)	Composite commodity (QQ)	Domestic demand (QD)	Exports (QE)	Imports (QM)
Agricultural commodities	− 1.05	− 0.22	− 0.40	− 6.48	2.74
Food commodities	− 0.48	− 0.11	− 0.28	− 3.65	2.36
Other commodities	0.04	− 0.03	− 0.01	0.33	− 0.20
Total	− 0.04	− 0.04	− 0.04	− 0.01	− 0.06

Despite the compounding effect of these two scenarios, the overall impact of the declines in world prices on the exchange rate is rather minimal, mainly because the actual magnitude of food and agricultural trade is small in relation to total trade (the exchange rate only depreciates by between 0.05 per cent and 0.23 per cent in simulations sim01 to sim05). Although negative, the impact on domestic consumption (QQ) is small due to the small income effect in this simulation. The international and domestic demand movements put pressure on demand for domestically produced commodities, as reflected in the decline in production of both food and agricultural commodities (QXC). These reductions cause overall production in the economy to decline only marginally by 0.04 per cent.

Despite this overall decline in production, the impact is not all negative for domestic producers. Some producers benefit from the lower import prices since a component of intermediate inputs is imported. This is reflected in the prices of intermediate inputs that decline for agricultural and food activities (not shown here). The overall decline in domestic production has a negative impact on the economy-wide employment. This is caused by the marginal decline in factor demand (FD) in the agricultural and food industries (see Table 8). Factor demand in other industries increases slightly as a result of the positive welfare effects associated with cheaper imported commodities, but this is not enough to counter the employment losses in the agricultural and food industries.

Table 8: Factor demand (FD) effects for a 4 and 2 per cent reduction in world agricultural and food commodity prices respectively (INTSET, sim04, percentage changes)

	Unskilled/unemployed		Medium-skilled/Fully employed			High-skilled/Fully employed
Factor groups	African	Coloured/Asian	African	Coloured/Asian	White	African	Coloured/Asian	White
FD (agric)	− 1.07	− 1.42	− 1.44	− 1.38	− 1.06	− 1.11	− 1.57	− 1.26
FD (food)	− 0.51	− 0.60	− 0.60	− 0.37	− 0.58	− 0.54	− 0.62	− 0.70
FD (other)	0.07	0.10	0.08	0.04	0.11	0.01	0.02	0.06
Total	− 0.04	− 0.08	0.00	0.00	0.00	0.00	0.00	0.00

Figure 3 summarises the impact on factor income (YF) for the various labour groups. The declines in the agricultural and food output of just over 1 per cent and nearly 0.5 per cent respectively are associated with aggregate employment reductions ranging from − 1.7 to − 0.2 per cent. The reductions vary widely, as do the factor employment intensities. The biggest losers are low-skilled coloured workers, many of whom are employed in the Western Cape, where a 1.6 per cent drop in agricultural production (QX, not shown) is experienced – slightly higher than the national average decline of 1.3 per cent. This region relies heavily on exports, which increases its sensitivity to world price changes.

Figure 3. Economy-wide factor income effects (YF) for a 4 and 2 per cent reduction in world agricultural and food commodity prices respectively (INTSET, sim04, percentage changes)

4.3.3 Combined domestic and international efficiency gains (COMSET)

In the third simulation set the outcome of simultaneous domestic and international agricultural technical change is evaluated. As with INTSET, the decline in world trade prices causes the exchange rate to depreciate. These trade price changes induce consumers to substitute domestically produced goods for cheaper imported goods, while domestic producers tend to allocate more of their production to the domestic market, where prices are now relatively higher.

There is also a domestic price impact associated with the efficiency gains in the agricultural sector. These domestic price movements counteract the domestic consumption and production substitution processes set in motion by the lower prices of imports and exports (as outlined in INTSET). The impact on the trade balance is thus greatly reduced (see Table 9, and compare Tables 5 and 7). In fact, there is an increase in agricultural exports but a decrease in food exports and vice versa for imports. Also note that the change in the quantity of domestically produced commodities (QXC) is lower than under the domestic efficiency gain simulation due to the negative impact of international price declines.

Table 9: Commodity flows for simultaneous domestic and international agricultural technical change (COMSET, sim04, percentage changes)

	Domestic production (QXC)	Composite commodity (QQ)	Domestic demand (QD)	Exports (QE)	Imports (QM)
Agricultural commodities	1.02	0.49	0.66	4.00	− 2.25
Food commodities	0.23	0.41	0.35	− 1.66	1.19
Other commodities	0.14	0.14	0.15	0.12	0.11
Total	0.18	0.17	0.18	0.17	0.11

Although Table 9 only reports the results of a 4 per cent increase in domestic efficiency, it is interesting to look at the entire range of productivity changes to determine the domestic efficiency gains that will allow the overall agricultural production effect to be positive. The results in Table 10 indicate that only at a 3 per cent efficiency gain will all domestic agricultural producers experience production growth that is sufficient to counteract the negative production effects associated with a 4 per cent (2 per cent) decline in the world prices of agricultural (food) commodities. At the economy-wide (total QX) level the agricultural sector ‘breaks even’ if domestic efficiency gains equal 2 per cent (sim02). Table 10 also shows that different regions are affected in different ways by these simulations; these differences are reflections of the differences in technologies used and commodities produced in the various agricultural regions. This highlights an important policy implication: the consequences of uniform technical progress are not necessarily uniform.

Table 10: Domestic agricultural production (QX) for a 4 and 2 per cent reduction in world agricultural and food commodity prices respectively, and domestic efficiency gains in all agricultural industries ranging from 1 to 5 per cent (COMSET, sim01–sim05, percentage changes)

	sim01 (1%)	sim02 (2%)	sim03 (3%)	sim04 (4%)	sim05 (5%)
Eastern Cape	0.14	0.46	0.78	1.11	1.44
Free State	− 0.81	− 0.15	0.51	1.18	1.85
Gauteng	0.72	1.23	1.75	2.27	2.79
KwaZulu-Natal	− 0.48	0.18	0.84	1.51	2.18
Limpopo	− 1.18	− 0.33	0.53	1.41	2.30
Mpumalanga	− 0.99	− 0.16	0.67	1.52	2.37
Northern Cape	− 0.81	− 0.18	0.46	1.10	1.75
North West	− 0.65	− 0.09	0.47	1.03	1.60
Western Cape	− 0.78	0.04	0.87	1.72	2.57
Total	− 0.64	0.05	0.74	1.44	2.15

Due to increased productivity, factor demand (FD) declines in all agricultural and food industries (see Table 11), but despite this the overall employment level of unskilled workers increases, mainly due to an increase in demand for factors in other expanding non-agricultural sectors. This increase in demand is reflected in higher wages for skilled workers and higher employment levels for unskilled workers (given the closure assumptions), thus leading to an overall increase in factor income (YF) for all workers (see Figure 4).

Figure 4. Economy-wide factor income effects (YF) for simultaneous domestic and international agricultural technical change (COMSET, sim04 percentage changes)

Table 11: Factor demand (FD) effects for simultaneous domestic and international agricultural technical change (COMSET, sim04, percentage changes)

	Unskilled/unemployed		Medium-skilled/Fully employed			High-skilled/Fully employed
Factor groups	African	Coloured/ Asian	African	Coloured/ Asian	White	African	Coloured/ Asian	White
FD (agric)	− 2.52	− 2.22	− 2.69	− 2.85	− 2.31	− 2.92	− 2.63	− 2.51
FD (food)	− 0.85	− 0.78	− 1.05	− 0.84	− 1.18	− 1.28	− 1.31	− 1.52
FD (other)	0.52	0.40	0.14	0.09	0.25	0.02	0.03	0.12
Total	0.23	0.10	0.00	0.00	0.00	0.00	0.00	0.00

As shown in Figure 4, the average factor income changes for aggregated factor groups range from 0.10 per cent to 0.64 per cent, with an average increase of 0.44 per cent. The largest decline for an individual factor account is 1.62 per cent (African low-skilled workers in the Eastern Cape). These translate into similarly small impacts on household incomes: the largest decrease in household income for a specific household group is 0.97 per cent (African agricultural households in KwaZulu-Natal), while the largest increase is 0.64 per cent (African high-income household in Gauteng). These income changes are by no means large, but simultaneously there are commodity prices changes that will have an impact on real incomes and hence it is worth considering the welfare implications.

4.3.4 Welfare implications of combined domestic and international efficiency gains

Among the results generated by the CGE model is a series of summary welfare measures based on the equivalent variation (EV), which takes into account both (household) income changes and price changes given consumers' consumption bundles. While these are useful summary statistics it is important that they are treated with caution because the economic theoretic properties of the measures strictly require the imposition of restrictive conditions in the model; despite this qualification they remain useful summary measures. The Slutsky approximation of the economy-wide ⁷ EV welfare measure generated by the model shows an increase from R490 million in sim01 to R3210 million in sim05 for the economy as a whole, clearly from an economy-wide perspective a positive result.

A substantive advantage of the PROVIDE database is the link between the SAM data on household incomes and expenditures and the Income and Expenditure Survey for 2000 (IES 2000 – see Stats SA, 2002) used to estimate the SAM. Previous simulations (not reported here), based on a more aggregated set of household accounts, indicated the relative disadvantage experienced by rural households vis-à-vis urban households as measured by equivalent variation welfare measures, mainly because the latter benefited from increased employment opportunities in non-agricultural sectors and lower prices. These results confirmed the potential for appreciable income and welfare distribution consequences and thereby indicated the potential benefits of a more disaggregated assessment of the income distribution effects. This assessment is limited to the COMSET series of simulations.

The method adopted for this study is an adaptation of a method first used by Adelman and Robinson (1978). Each household in the IES 2000 is linked to one of the 162 household groups in the SAM. ⁸ Because of this linkage, changes in the incomes of the representative household groups can be related to the original households in the survey. The method used here makes the assumption that the income of each household in the survey database changes by the same proportion as the income of the linked representative household in the model. Poverty and inequality estimates are then calculated directly from the new per capita income estimates and any changes are analysed in a comparative static fashion. ⁹

There are two practical approaches to account for price changes. In the first approach the poverty line can be adjusted by reference to the national price level, i.e. the national CPI, which by construction in the CGE model is the numéraire and hence fixed. However the national CPI is weighted using national average consumption patterns, which means that the ‘real’ household incomes in the model do not reflect differences in household consumption bundles and preferences. An alternative approach is to adjust each household's poverty line by a household-specific CPI generated by the model; these are price indices for each household group that take into account household-specific consumption bundles. These CPI measures change as prices and consumption bundles change due to income changes as well as substitution processes associated with utility maximisation and vary appreciably across household groups. This second approach is used here. The household-specific CPIs are then used to generate estimates of real household incomes. A poverty line of R3864 per capita per annum is used throughout to assess changes in poverty rates (based on Hoogeveen & Özler, 2005).

Figure 5 summarises the changes in the poverty headcount ratios in urban and rural areas for the five simulations in COMSET. In all instances household incomes are either unadjusted or adjusted using the household specific CPIs. Although the changes are small (take note of the scale on the vertical axis) two important points can be made: firstly, overall poverty in urban and rural areas declines from the base level as a result of agricultural efficiency gains. This implies that the decline in income resulting from job losses is offset by increases in income associated with more non-agricultural jobs in the economy, even in rural areas. Secondly, when adjusting the poverty line with the household-specific CPI measures the poverty-reduction impacts are larger. This implies that the food price reductions have an important impact on households close to the poverty line, a result which is expected given that low-income households spend a greater proportion of their budgets on food items.

Figure 5. Poverty headcount ratios in urban and rural areas for simultaneous domestic and international agricultural technical change (COMSET, sim04 percentage changes)

Given the small changes in income levels the overall inequality impact is also small. Figure 6 shows the changes in the Gini coefficient for the five simulations in COMSET. Using the per capita income distribution South Africa's base-level Gini coefficient is 0.6897. This rises marginally to about 0.6899 in sim05, which suggests that households affected by job losses (and hence income losses) in the agricultural and food production sectors are lower down the welfare ladder than those households that gain from additional employment opportunities in non-agricultural sectors. However, if the per capita income measure is adjusted by the household-specific CPIs, the Gini coefficient actually declines marginally, which suggests that low-income households, given their consumption bundles, benefit relatively more as a result of biased price changes.

Figure 6. Changes in inequality as measured by the Gini coefficient for simultaneous domestic and international agricultural technical change (COMSET, sim04 percentage changes)

An interesting and important insight is provided by the results for sim01 and sim02, i.e. simulations that imply a relative decline in the international competitiveness of South African agriculture. The urban households benefit in all scenarios, which is unsurprising since a primary reason for their reduction in the poverty headcount is the decline in food prices that occurs whether or not South African agriculture increases its efficiency. But the rural households experience an increase in the poverty headcount under sim01, which also produces the largest CPI-adjusted Gini coefficient. From sim02 onwards both the rural poverty headcounts and the CPI-adjusted Gini coefficient progressively decline. This confirms the expected importance of improving the efficiency of South African agriculture. However, even if domestic agricultural efficiency gains are not realised there are still potential welfare gains from efficiency gains that originate overseas.

5. Conclusions

Producers, and in particular agricultural producers, face production declines when foreign agricultural producers achieve relatively faster efficiency gains. It is therefore important for domestic producers to counteract this decline in competitiveness by also increasing productivity. Any improvement in relative efficiency is likely to allow greater penetration of export markets, while domestic price reductions will stimulate increases in domestic demand. As the simulations illustrate, domestic and international agricultural efficiency gains will induce the agricultural industry to reduce employment. The important lesson is that the achievement of greater efficiency in agricultural production almost invariably implies that employment in agriculture will decline unless the growth in total demand is sufficiently large to offset the (direct) decline in employment due to efficiency gains. This will probably only occur in the unlikely event that export demand expands substantially, since demand for food and agricultural commodities is income-inelastic. This is not the case in the simulations reported in this paper, but even so the overall employment and wage effects are positive due to increases in demand for factors in other industries that benefit indirectly from the efficiency gains in agriculture.

Although the job losses are made up for in other industries it is important that government recognises the existence of an adjustment period. Recognition of such will allow it to address the resultant issue of job opportunities in rural areas where most of the job losses are likely to occur, and thereby attempt to ameliorate the adverse effects on some members of society while still reaping the substantial welfare gains. As far as the distributional outcomes of agricultural efficiency gains are concerned, it was shown that when household incomes were adjusted by their respective CPIs, poverty was reduced by a greater margin. This adjustment also reduces income inequality.

This study demonstrates that even moderate efficiency gains in South African agriculture can be expected to produce appreciable welfare gains, despite agriculture being responsible for only about 3 per cent of GDP. Moreover, it is shown that the benefits from domestic efficiency gains are not nullified by international efficiency gains; the combined effects still result in small but important welfare effects in the South African economy. Under all the scenarios reported here, whether international trade prices of food and agricultural commodities decline, or whether domestic agricultural producers experience efficiency gains, consumers benefit from lower prices of especially agricultural goods and, to a lesser extent, food products. For the average household, income increases (or remains virtually unchanged) and prices decline, which means that the welfare effects associated with both types of efficiency gains are positive.

However, the results from the poverty analyses demonstrate that the impacts on rural and urban households differ. The urban households experience a decline in the poverty headcount under all scenarios and all rates of efficiency gain, but unless efficiency gains in South African agriculture are sufficiently rapid the poverty head count in rural areas will increase, and this increase is likely to be sufficiently large to generate increases in inequality.

The policy implications are clear. Attempts to maintain rural employment through resisting technical progress are likely to fail from a welfare perspective as long as South Africa's trading partners become progressively more efficient. The analyses indicate that the government should seek to raise the rate of technical progress despite the employment-reducing effects. Such an increase in efficiency will help maintain competitiveness while reducing the cost of living and thereby improving welfare. While rural poverty may be adversely affected by rising rural unemployment, the opening up of new opportunities elsewhere in the economy may well outweigh the job losses. The government can help address the rural unemployment problem by assisting the process of rural–urban migration and/or encouraging the development of new opportunities outside the traditional urban centres. Since even small changes in agricultural efficiency produce substantive welfare benefits it is consequently crucial that the government does not introduce policies that adversely affect the performance of agriculture without first assessing the overall consequences.

Additional information

Notes on contributors

Cecilia Punt

Respectively, Senior Researcher, Development Policy Research Unit, University of Cape Town and Research Associate, PROVIDE Project, Elsenburg, South Africa; Reader in Economics, Department of Economics, University of Sheffield (UK) and Technical Expert, PROVIDE Project; and Manager: Macroeconomics Division, Western Cape Department of Agriculture and Project Leader, PROVIDE Project.

Notes

¹Defined in this context as change in the flow of factor services from a unit, measured in ‘natural’ units, of the factor.

²The modelling of production relationships in the CGE is discussed in detail in Section 3.4 of PROVIDE (2005a: 22–5).

³A variant of the PROVIDE CGE model with multiple trade partners could have been used to provide insights into the impacts on trade patterns, but this was not undertaken since it would have required detailed data and/or assumptions about price changes across trade partners.

⁴A full set of results for this study is available from the PROVIDE website – http://www.elsenburg.com/provide – together with the requisite software.

⁵The same patterns are repeated for the other simulations and hence only the results with unemployed unskilled labour and a fixed government deficit are reported subsequently.

⁶The CGE model is of course unable to tell us more in this regard.

⁷Based on final demand by all domestic institutions, i.e. households, enterprises, government and investment.

⁸For a detailed description of the formation of these representative groups refer to PROVIDE (2005a). Another matter worth mentioning is the data quality concerns of the IES 2000. This dataset is fraught with data problems, which makes estimates somewhat unreliable. Most of the problems relate to sloppiness in data collection, accounting and coding of variables. There are also numerous records that are problematic due to missing values for some of the variables, while an alarmingly large number of households report zero expenditure on food. Reporting on, for example, tax payments is also far below the expected level when compared to actual tax collection data. Many of these data problems were addressed by making adjustments to the data, imputing missing values or correcting implausible ones, and so on, especially in the case of food and tax expenditure estimates. A detailed account of the adjustments made is included in PROVIDE (2005b).

⁹Adelman and Robinson (1978) used data on the mean and variance of the representative household groups and then estimated the change in poverty by adjusting the means with constant variances.