## Ephraim Chirwa and Andrew Dorward

Print publication date: 2013

Print ISBN-13: 9780199683529

Published to Oxford Scholarship Online: January 2014

DOI: 10.1093/acprof:oso/9780199683529.001.0001

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# Benefit–cost analysis, 2006/7 to 2010/111

Chapter:
(p.196) 9 Benefit–cost analysis, 2006/7 to 2010/111
Source:
Agricultural Input Subsidies
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199683529.003.0009

# Abstract and Keywords

This chapter develops benefit–cost estimates for the Malawi Farm Input Subsidy Programme. It argues the need for caution in comparing estimates across different investments as analyses often include and exclude different benefits, and use of the standard partial equilibrium methods for benefit–cost analysis of agricultural input subsidies does not take into account wider benefit to poor consumers and the economy from lower food prices. Demand and supply curve analysis is used to estimate ‘without subsidy’ prices and producer and consumer gains for benefit–cost analysis without and with allowance for further gains from consumer expenditure linkages or growth multipliers. Average benefit–cost ratio (BCR) is likely to be around 1.35, depending on assumptions, with BCR above unity estimated in all years except 2008/9, when there were very high fertilizer prices. The analysis suggests attention to raising yield responses, targeting and a balance of complementary investments to raise programme returns.

# 9.1. Introduction

In this chapter we develop benefit–cost estimates for the FISP, using methods that have relatively simple analytical and data demands (to allow their application in practical policy analysis) but nevertheless yield reasonably robust estimates that allow valid comparisons with estimates of the costs and benefits to potential alternative investments.

The chapter is structured as follows. After this introduction we first consider the purpose and principles for benefit–cost analysis (BCA) and common methods used in BCA. We then review problems and challenges identified with previous BCA on the FISP. This leads on (in Section 9.5) to technical suggestions for methodological improvements in estimating benefit–costs of FISP and we then apply these methodologies to estimate returns to investment over the life of the programme. Readers without a particular methodological interest in benefit–cost analysis may like to skip this section. We conclude with a discussion of the implications of the analysis for FISP’s design and implementation.

# 9.2. Benefit–cost analysis purposes and principles

Benefit–cost analysis (BCA) of input subsidy programmes has two main functions.

• It gives an indication of the returns to specific programmes as compared to returns that might be achieved from alternative investments, and can thus guide overall government investment and spending decisions. Estimates of such returns are also commonly used for more (p.197) general comparisons of the returns to different types of investments (for example, between agricultural input subsidies, research, and infrastructural development) in order to guide investment choices between programmes.

• It provides information about the variables that are important in determining costs and benefits of a specific programme or type of programme, and hence can guide programme design and implementation decisions to increase benefits relative to costs.

These two uses of BCA are both important, but they present analysts with something of a dilemma. The first requires the use of common standards across different programmes, perhaps in different sectors, to give comparable results across investment alternatives. These standards generally involve standardized methods, but it is often difficult to apply such methods across programmes that affect people and the economy in different and complex ways and in different policy contexts. These difficulties need to be recognized when making comparisons between BCA results obtained for different programmes. The second purpose of BCA requires not so much standards for comparable estimates of returns, but accurate estimates of the relative importance of different variables affecting these returns in particular investments—and here there may be more value in tailoring methods to match specific programme features. This, however, leads to a danger that the results may not be comparable with results from analysis of other investments, but may nevertheless be (wrongly) used for making such comparisons.

Taking these two purposes together with an overall objective that BCA should provide rigorous, reliable, and objective estimates of benefits and costs, we suggest the following seven principles for the choice and implementation of BCA methods (these are not set out according to any prioritization). BCA methods applied in any situation should be

1. 1. Practicable: They must be applicable to the data and analytical resources (skills and software, for example) that are available (or can reasonably be obtained).

2. 2. Externally consistent: They must provide measures that are comparable with generally accepted good practice in definitions of costs and benefits (for example, in definitions of financial and economic benefits).

3. 3. Contextualized: They must take account of particularities that affect the benefits and costs of a programme as regards the processes by which costs and benefits are linked, the effects of other policies and investments on these, and the conditions affecting these.

4. (p.198)
5. 4. Holistic: They must take account of all the significant benefits and costs associated with a policy or investment programme, both direct benefits and costs to recipients or beneficiaries and indirect benefits and costs to others.

6. 5. Internally consistent: They must properly represent the significant relationships between investments and behaviours by different stakeholders, taking account of ‘counterfactuals’ (comparing actual behaviours and outcomes under a programme or investments against those that would have occurred in its absence).

7. 6. Transparent: Assumptions, measures, data sources, shortcomings, and possible bias and inaccuracies in methods and their results must be stated and discussed.

8. 7. Cost-effective: BCA methods should be chosen, developed, and implemented to ensure that costs of analysis are commensurate with the value of the information provided.

The cost-effectiveness of methods is of course affected by the costs of BCA methods in providing information and in value of the information provided.

• Costs are determined by resource demands for gathering extra information needed and for analysis (as discussed above under practicability and as we discuss below as regards demands for different methods).

• The value of the information provided is determined by its quality and by the scope for its use.

• The determinants of quality are external and internal consistency, holism, and contextualization (as discussed above) and the strengths and weaknesses of analytical methods (which we discuss below).

• Scope for use of information is determined by transparency of results (as discussed above), by the strengths and weaknesses of different methods (which we discuss below), and by the potential ‘decision space’ for changes in policy choices, design, and implementation in the light of new information provided by BCA.

There are particular challenges in applying the first four of the principles above to the specific situation in which the FISP operates.

1. 1. Practicable. There are severe limitations in data availability (for example, on crop areas and yields, the yield and production effects of subsidized seed and fertilizer, and the number of farm families in the (p.199) country). There are also limited financial and human resources available for analysis, but the determination of the ‘counterfactual’ situation of what would have happened without a subsidy is very complex, properly requiring consideration of changes throughout the whole economy as a result of changes in farm incomes, in food prices, and in the real incomes of consumers. The data and resource limitations lead to a fundamental question about the practicability of making any reliable estimates without substantial improvements, particularly in data availability.

2. 2. Externally consistent. Limited availability of good quality data poses problems for the application of good practice in BCA. A further difficulty arises with the longstanding history of policy interventions inhibiting maize imports and exports, as this makes it very difficult to identify true economic prices for maize—conventionally, import and export parity prices should be used in economic analysis, but one may legitimately ask if liberalized market policies are a real policy option for the Malawian Government (see Tschirley and Jayne (2010) for a nuanced discussion of these issues). If import parity prices are to be used in the analysis then it is very difficult to determine what national prices would actually have prevailed with and without the subsidy (this adds to the already difficult task of estimating counterfactual ‘without subsidy’ prices for comparison against the ‘with subsidy’ situation—a ‘double counterfactual problem’).

3. 3. Contextualized. The effects of the subsidy on livelihoods are complex, widespread, and in many ways specific to the problems faced by poor Malawian smallholders (with the low maize productivity trap and policy context discussed in Chapter 4). Analysis has to take account of these contextual issues—but this may lead to conflict with the two previous principles—requiring more complex, non-standard analysis.

4. 4. Holistic: The scale and nature of the FISP means that it has widespread, complex, and varied effects on the livelihoods of different farm households, on consumers, and on maize and labour markets. Ideally this requires holistic consideration of dynamic and interacting changes in rural livelihoods and in rural and national markets. This presents very large data and analytical challenges. This is clearly related to the problems of contextualization, with similar potential for conflict with the principles of practicality and external consistency—for example: can simpler methods be modified to represent key effects of wider, complex changes and also generate results that allow meaningful comparison with BCA on other investments? (p.200)

# 9.3. Benefit–cost analysis methods

Investment and policy analysis methods can be classified according to the extent to which they focus on direct, ‘partial equilibrium’ effects of an investment or policy on the beneficiaries in the relevant sector as against wider, indirect ‘general equilibrium’ effects on beneficiaries and non-beneficiaries across all sectors in an economy. Increasing consideration of wider indirect effect increases the analytical complexity and data requirements. However although these effects may not be important for smaller scale interventions, they may dominate the direct effects for large-scale investments in the agricultural sector if these affect food prices and the productivity of large areas of land and large amounts of labour. Where more complex and demanding general equilibrium methods are used, these should properly represent markets’ and different stakeholders’ behaviours and interactions. Where more simple partial equilibrium methods are used, then these should where possible build in simple adjustments to simulate possible wider economy effects.

It is helpful to distinguish between three basic methodological approaches to BCA for large-scale policy investments:

1. a) Regression models which estimate returns to investments by analysing comparative data sets across different regions in a country, for example, and estimate the impacts of investments on welfare measures or economic growth (for example, Fan et al. (2007)), implicitly taking account of multipliers and wider general equilibrium market effects.2

2. b) Computable general equilibrium (CGE) and multi-market models that analyse the effects of investments by simulating economic behaviour with and without investments—with general equilibrium models simulating economy-wide effects, and multi-market models examining effects across a more restricted set of markets (for example, Buffie and Atolia (2009) use a CGE analysis of the Malawi FISP to consider the relative benefits of investment in the FISP against investment in infrastructure, but do not undertake a formal BCA of the FISP).

3. c) Partial equilibrium models that examine investment’s welfare impacts on producers and consumers (see, for example, C. P. Timmer (1989) for Indonesia).

(p.201)

Table 9.1. Broad characteristics of three model types

Regression models

CGE/Multi-market models

Partial equilibrium models

Data demands

Very challenging: time series data for different & relatively independent regions: investment, welfare & other variables

Very challenging: national & multi-sectoral data on supply, demand, productivity, market performance, & factor ownership; direct productivity impacts of investment/policy interventions

Demand (& ideally supply) information on specific commodity/ies of interest; direct productivity impacts of investment/policy interventions

Capacity to describe multi-market, indirect effects

Good: intrinsic in analysis of broader welfare effects

Good: the key benefit of these models, but depends on quality of model formulation & data

Weak: no explicit consideration, but can introduce ad hoc adjustments to allow for these effects

Capacity to describe differential market failure effects

Good: should be intrinsic in analysis of broader welfare effects but may not capture some spillovers

Weak: very challenging as regards data demands & model formulation

Weak: no explicit consideration, but can introduce ad hoc adjustments to allow for these effects

Capacity to isolate effects of specified intervention(s)

Depends on range of conditions in data set—difficult if covariant changes or if there are varying spillovers across regions

Good, depending on quality of model

Can be good, depending on context & processes

Strengths

Good data sets & properly executed analysis can give very holistic empirical analysis

Multi-market effects, counterfactuals

Relatively simple data & methodological demands

Weaknesses

Very demanding requirements as regards historical/empirical data sets—this can limit breadth of application of models; assumptions/context may not be explicit or generalizable; may not account for some spillover effects

Complex & demanding; proper representation of market failures & differential behaviour of producers & consumers very challenging—otherwise misleading; assumptions/context may not be explicit

Does not take account of market effects—these can only be addressed with simple relatively ad hoc adjustments

These models differ as regards their data demands, the nature of the analytical challenges they present, and their ability to allow for market failures, differential effects on different types of consumers and producers, linkages and (p.202) multipliers across markets, and the interactions between these. Table 9.1 sets out the broad characteristics of these three types of model.

It is clear from Table 9.1 that the three different approaches have different and in many ways complementary features, strengths, and weaknesses. We can conclude from this that

• In different contexts there will be different choices of method to best follow the principles outlined earlier.

• In all cases analysts must recognize and take account of the limitations of their methods and data, and document these to ensure that those using their results are able to properly interpret them.

• Those using BCA results to compare returns from different investments or to guide policy or investment design and implementation must take great care to ensure that differences in analytical methods, issues, and data quality are properly allowed for in their considerations.

• In the particular situation of the Malawi FISP

• it is impossible to conduct regression analysis as the empirical situations and data available do not allow this;

• CGE and multi-market models are very demanding of analytical resources and data, and consequently these models may be used for stylized analysis of possible effects, but will be too expensive in implementation, too complex in application/interpretation, and too reliant on weak data to provide a practicable method for regular and detailed year by year analysis;

• the more limited data and analytical demands of simpler partial equilibrium models mean that they are the most practicable (though there are still significant challenges here).

# 9.4. Problems and challenges with benefit–cost analysis (BCA) of the FISP

Dorward and Chirwa (2009, 2010a) and School of Oriental and African Studies et al. (2008) have used standard partial equilibrium methodology for estimating the economic benefit–cost ratio and fiscal efficiency of the subsidy programme. They recognize, however, that this method does not take account of wider benefits to poor consumers from lower food prices, and that paradoxically a greater fall in the price of maize provided a lower estimate of programme benefit when in fact larger price falls should lead to wider growth and poverty reduction benefits. They also consistently identify (p.203) a number of concerns with the use of their results in comparing estimated returns from subsidies and from other investments. These concerns are also relevant to the limited reports of benefit–cost and related analysis by others (For example Buffie and Atolia (2009) and Denning et al. (2009)) and to discussion of these results.

The concerns may be broadly classified into related problems first with data, second with methodology, and third with wider theoretical issues. These problems are of course related, as

• methodologies embody theory and require, and are limited by, data, and

• theories require, and are embodied in and limited by, methodologies.

The three major theoretical questions concern

1. (a) the measure of benefits,

2. (b) the extent of benefits and processes of change, and

3. (c) the valuation of incremental production.

The measure of benefits: Ideally benefits should represent welfare changes to recipients and non-recipients. This, however, raises questions about the nature of welfare, methods of measurement or estimation, and the relative importance and weighting of welfare changes for different stakeholders (for example, questions about the relative importance of welfare changes in poorer and less-poor people, and about the relative importance of welfare changes in people now and in the future). Economic theory provides widely used measures of welfare changes through the concepts of consumer and producer surplus. There are, however, severe methodological and data difficulties in the estimation of supply curves needed for the estimation of changes in producer surplus. As a result, changes in real income are commonly used as proxy measures of welfare in benefit–cost analysis, and generally provide similar answers (Sadoulet and de Janvry, 1995; Alston et al., 2000). The relatively simple analysis in School of Oriental and African Studies et al. (2008), Dorward and Chirwa (2009), and Dorward et al. (2010a) provides reasonable estimates of changes in aggregate real income across producers and consumers, but no information about the distribution of these benefits between producers and consumers or between beneficiaries and non-beneficiaries. This differentiation is important for the use of weights to address distributional questions about welfare changes for different types of people.

The extent of benefits and the processes of change: We argued in Chapters 2 and 4 that subsidy programme benefits can have wide-ranging and far-reaching dynamic effects where they directly overcome financial market failure and investment affordability problems of recipients, and address these same problems for poor non-recipients through staple food prices and higher wages; (p.204) and that they should also generate more conventional multiplier growth effects (where, for example, increases in recipients’ income lead to increases in consumption of locally produced goods and services, and hence increases in incomes for local providers of these goods and services). Haggblade et al. (2007a) suggest agricultural multipliers (excluding dynamic effects from overcoming market failures) range from 1.3 to 1.5 in sub-Saharan Africa, while Davies and Davey (2008) report estimated multipliers of 2 to 2.45 from conditional cash transfers in Dowa (though these fixed price estimates may be reduced by 30% to allow for supply constraints, to give estimates of 1.4 to 1.7). Diao et al. (2003) estimate a multiplier of 1.5 from increases in grain productivity in Malawi while Benin et al. (2008) estimate a multiplier of 1.1 from increases in maize productivity in Malawi.

Dynamic effects and multipliers are implicitly allowed for in BCA using regression analysis (for example, Fan et al. (2007)), and they should be explicitly modelled in general equilibrium analysis, although this is seldom the case for the dynamic effects of overcoming market failures. Multipliers and dynamic effects are not allowed for in estimates derived from partial equilibrium methods, and this leads to a biased under-estimate of returns when these estimates are compared with estimates of other investments’ returns if these estimates are derived from regression or general equilibrium analyses.3

The valuation of incremental production: The concerns discussed above about the measure of benefits and their extent and distribution are concerned with the valuing of incremental production, in a very broad sense. Here, however, we discuss two narrower issues: first the choice of prices for valuing output and second the discount rate to use.

As noted earlier, there are legitimate questions about the feasibility of liberalized market policies as a real policy option for the Malawian Government, and hence if economic analysis should use border or domestic prices. Either way there are then serious methodological challenges in determining ‘counterfactual’ prices for a situation without the subsidy (with a ‘double counterfactual’ problem if combinations of domestic and border prices are to be used). Dorward et al. (2010a) and School of Oriental and African Studies et al. (2008) use information on border prices with informed judgement to address the ‘double counterfactual’ problem to estimate what border prices would have prevailed with and without the subsidy in the absence of policies restricting imports. (p.205)

They also do not use an explicit discount rate when comparing programme benefits and costs. However any comparison of the programme’s benefit–cost ratio with internal rates of return estimated for longer term investments involves an implicit assumption that benefits are achieved one year after investment. It might, however, be argued that costs are incurred in December to January (when seeds and fertilizers are paid for and applied to the field) but benefits are obtained in June (when crops are harvested), giving a return after 6 or 7 months. It might also be considered, however, that benefits from lower maize prices and increased consumption are enjoyed over the period June to May, yielding a return over an average of around 12 months. These two alternatives have major implications for estimates of internal rates of annual return, as the former has a net Internal Rate of Return (IRR) 70–80% higher than the net benefit–cost ratio (BCR, net benefits divided by costs).

The discussion above addresses theoretical and related methodological concerns with the standard use of partial equilibrium analysis in BCA for the FISP. These concerns are exacerbated by and linked to difficulties with the quality and availability of critical data on yield responses to subsidized inputs, on overall production data, and on the number of rural and farm households—difficulties that have been noted repeatedly in earlier chapters.

# 9.5. Improving FISP benefit–cost estimates4

Consideration of these theoretical, methodological, and data difficulties together with the earlier discussion of purposes and principles for BCA suggests a number of approaches to improving the BCA of the subsidy programme. These involve

1. Continued use of partial equilibrium analysis, with its relatively limited demands for data and analytical resources, but with more formal counterfactual price estimation.

2. Extension of the method to distinguish between producer and consumer gains and, among producers, between subsidy recipients and non-recipients.

3. Consideration of possible dynamic effects of growth and liquidity multipliers.

4. Consideration of results with alternative estimates of the time period for returns. (p.206)

All these approaches involve elaboration of the estimation of programme benefits, as estimation of programme costs is not conceptually problematic (although, as discussed in Chapter 5, there are difficulties in obtaining reliable data on some cost items). Total costs incurred in input acquisition (including transport and distribution costs) are added to programme administration costs, with application of shadow exchange rates to non-tradable costs in the later years of the programme when the Malawi Kwacha is generally considered to have been over-valued. Costs of acquisition for subsidized inputs that displace unsubsidized inputs are subtracted from the programme costs, as these provide no incremental benefits and are simply a transfer from government to the recipients of those subsidized inputs. Although they consequently have little effect on the benefit–cost ratio of the programme (being excluded from both benefits and costs), they do affect the Net Present Value (NPV) of the programme, and hence its fiscal efficiency (which we define as NPV/fiscal costs).

## 9.5.1. Methodology for formal estimation of prices and producer and consumer gains

To improve on existing estimates of programme benefits we therefore begin by formalizing price estimation, focusing on the effects of the subsidy programme on maize production.5 Figure 9.1 shows how for an autarchic economy6 a production subsidy causes a downward shift in the market price supply curve (S to S*) and this leads to an expansion in supply (from Q to Q*) and a fall in consumer price for the product (from P to P*).

The change in real income for producers is analysed in terms of the effects of changes in output prices, costs, and volumes produced and sold.

(9.1)
$Display mathematics$

(9.2)
$Display mathematics$
(p.207)

Figure 9.1. Input subsidy impacts on output supply and price Source: Adapted from Dorward (2009b).

where Y P * = producers’ income after subsidy

Y P = producers’ income before subsidy

Q* = production after subsidy

Q = production before subsidy

P* = output price after subsidy

P = output price before subsidy

ΔQF = increase in production from use of subsidized inputs

C = producers’ average unit costs for output before/without subsidy

C * = producers’ unit costs for extra output (i.e. excluding subsidized costs)

The change in producers’ income therefore consists of changes in sales value less the costs of production with the subsidy, plus the savings on unsubsidized production where this has been displaced by subsidized production. The change in sales value is made up of a loss due to the fall in product price for the original amount produced (area abdf in Figure 9.1), but a gain from extra production at the lower price (area dchg in Figure 9.1).7 With totally elastic demand there would be no price loss and all the subsidized production would be extra production, hence under these circumstances (p.208) $Δ Y P = ( Q * − Q ) P * − Δ Q F C *$. (With totally inelastic demand there would be no increase in production and all the subsidized production would displace unsubsidized production, hence $Δ Y P = − Q ( P − P * ) + Δ Q F ( C − C * )$. Under these circumstances $Δ Y P = 0$ and hence

$Display mathematics$
The change in real income for consumers consists of the savings on existing purchases due to the price fall (abdf in Figure 9.1) plus the savings in extra purchases which are best valued in terms of savings on previous expenditures (area bcd in Figure 9.1).

(9.3)
$Display mathematics$

Total change in producers’ and consumers’ real income can be estimated by the sum of changes in producer and consumer incomes:

(9.4)
$Display mathematics$

The method for estimating overall benefits in equation 9.4 is broadly that used in Dorward et al. (2010a) and School of Oriental and African Studies et al. (2008). They use analysts’ informal judgement of ‘double counterfactual’ prices with and without the subsidy respectively to estimate P* and P in the absence of government bans on formal imports. P can, however, be estimated using formal estimates of price elasticity of demand (E D), together with information on prices and production with the subsidy. (P ‒ p*) can then be substituted as follows:

(9.5)
$Display mathematics$

We can then substitute for (P ‒ p*) into equations 9.2, 9.3, and 9.4 as follows:

Change in producer real income

(9.6)
$Display mathematics$
(p.209)

Change in consumer real income

(9.7)
$Display mathematics$

Change in producer and consumer real income

(9.8)
$Display mathematics$

Equations 9.6 to 9.8 still present problems in that we require an estimate of (Q *Q). However, the seasonal separation of supply and demand means that if we can initially ignore farmers’ expectations of lower prices in the following season then incremental production will be equal to the increase in production from use of subsidized inputs, so that (Q *Q) = Δ. Introducing this into equations 9.6 to 9.8 gives the following estimates of changes in real income:

(9.9)
$Display mathematics$

(9.10)
$Display mathematics$

Change in producer and consumer real income

(9.11)
$Display mathematics$

All of the analysis in this section has been derived from our initial consideration of a closed economy (Figure 9.1). It does, however, also apply to a small open economy with a wide band between import and export parity prices. Thus, if increased production causes an economy to eliminate imports of Q M so that the price falls to P*, below import parity P M, then this can be handled by estimating gains in consumer and producer real incomes allowing for these prices.8 (p.210)

In these circumstances then assuming that $( Q * − Q ) = Δ Q F$ as above then

(9.12)
$Display mathematics$

(9.13)
$Display mathematics$
and
(9.14)
$Display mathematics$

Use of equations 9.9 to 9.11 or 9.12 to 9.14 depends on the relative values of PM and P: equations 9.9 to 9.11 are used if PM 〉 P, and equations 9.12 to 9.14 are used if PM 〈 P, where P is estimated from equation 9.5. If, in addition, PM 〈 P* then PM replaces P* in equations 9.12 to 9.14, and there are no consumer benefits or producer losses from price changes. The equations above can also be adjusted to allow for exports if P* is below the export parity price PX . In this case PX replaces P* in equations 9.12 to 9.13 if the subsidy would move domestic prices from above import parity to below export parity prices, or in equations 9.2 to 9.3 (with replacement of $( Q * − Q )$ by $Δ Q F$) if the subsidy would move domestic prices which are already import parity to below export parity.

The methodology developed in this sub-section demonstrates the basic validity of the BCA approach used in Dorward et al. (2010a) and School of Oriental and African Studies et al. (2008), but also allows a breakdown between producer and consumer benefits with more formal estimates of P and Q* if estimates of $Δ Q F$ and of price elasticity of demand (E D) are available.

## 9.5.2. Estimation of price/quantity demand relations and of incremental production

We now develop estimates of overall returns to the subsidy and of separate producer and consumer benefits using the methodology developed above. First, however, estimates are needed of price elasticity of demand (E D) and of $Δ Q F$. These estimates are unfortunately not without their own difficulties.

We first consider the estimation of price elasticity of demand (E D) or (more generally) of the relationship between price and quantity demanded. Figure 7.4 in Chapter 7 shows maize prices and estimated quantities consumed per capita. This highlights an apparent discrepancy between the 1993/4 to 2005/6 and 2006/7 to 2010/11 data sets, with higher prices in the latter set. Possible (p.211) explanations for this were discussed earlier in Chapter 7, but it raises wider questions regarding the impact of increases in production on maize prices. If production estimates from 1993/4 to 2005/6 are broadly correct, then this suggests that the 1993/4 to 2005/6 data should provide a reasonable estimate of price elasticity of demand with constant wages—although there may be upward shifts in demand when wages rise.

Three regression models were estimated of log quantity on log price quantity from maize price data and supply estimates from 1993/94. The first is derived from data from the 1993/4 to 2009/10 seasons with the inclusion of a dummy variable for subsidy effects from 2005/6 onwards and a time variable to allow for changing base per capita demand over time. This gave an estimate of price elasticity of demand of –0.24 (n = 17, t = 1.5, R2= 0.56). Given concerns about the reliability of data from 2006/7 to 2009/10 as discussed above, and implausibly high estimates of ‘without subsidy’ prices when subsequently applying this model, it was rejected. The second model regressed log quantity on log price quantity from the 1993/4 to 2005/6 seasons9 and gives an estimate of price elasticity of demand of –0.38 (n = 13, t = 1.9, R2= 0.24). The third used the same data set with the inclusion of a time variable to allow for changing base per capita demand over time, and gives an estimate of price elasticity of demand of –0.51 (n = 13, t = 2.2, R2= 0.33). The third model was preferred as regards its better fit and inclusion of a time effect, and was therefore used in the analysis that is reported below and is shown in Figure 7.4.

Having considered the estimation of the relationship between price and quantity demanded and hence of price elasticity of demand (E D), we now consider the estimation of $Δ Q F$ incremental production from the subsidy programme. The difficulties of obtaining reliable and precise estimates of $Δ Q F$ were discussed earlier in Chapter 6. As noted there, Dorward et al. (2010a) and School of Oriental and African Studies et al. (2008) have therefore estimated incremental production assuming that every kg nitrogen (N) in incremental fertilizer application leads to 12 kg incremental grain production when applied on local maize and to 18 kg incremental grain production when applied on hybrid maize.10 This approach was also followed here, with incremental fertilizer application as a result of the subsidy programme estimated from 2006/7, 2008/9, and 2010/11 survey estimates of displacement of unsubsidized fertilizer sales by subsidized fertilizer sales. (p.212)

Table 9.2. Base benefit–cost analysis, 2005/6–10/11

Year

ED

P

P*

PM

PX

BASE BENEFITS

US$/kg Net benefit BCR FE (US$ mill)

2005/6

0.51

0.24

0.14

0.29

0.14

12.4

1.17

0.34

AE

mean =

0.14

n/a

n/a

-7.6

0.90

-0.21

2006/7

0.51

0.25

0.13

0.32

0.17

47.8

1.49

0.65

AE

mean =

0.15

n/a

n/a

6.0

1.06

0.08

2007/8

0.51

1.83

0.35

0.30

0.15

39.4

1.30

0.41

AE

mean =

0.25

n/a

n/a

8.9

1.07

0.09

2008/9

0.51

1.16

0.25

0.28

0.13

-39.0

0.87

-0.16

AE

mean =

0.28

n/a

n/a

-40.2

0.87

-0.16

2009/10

0.51

0.46

0.17

0.28

0.13

31.9

1.18

0.23

AE

mean =

0.26

n/a

n/a

35.4

1.20

0.25

2010/11

0.51

0.95

0.19

0.35

0.20

127.9

1.55

0.88

AE

mean =

0.30

n/a

n/a

106.0

1.46

0.73

Notes: ED , P, P*, PM, and PX represent respectively demand elasticities, without and with subsidy maize prices (in current US$), and import and export parity maize prices (calculated from SAFEX prices with import and export transport costs of$100/MT and $50/MT respectively). BCR (benefit–cost ratio) is calculated as total economic benefit divided by total economic costs; FE (Fiscal Efficiency) as net benefit (total economic benefit less total economic costs) divided by total fiscal costs. Under ED , ‘AE’ stands for Analyst Estimates as reported in Dorward et al. (2010a) and School of Oriental and African Studies et al. (2008). ‘n/a’ indicates ‘not applicable’ ## 9.5.3. Formal estimation of prices and producer and consumer gains Using these estimates of the relationship between price and quantity available and of the incremental production from the subsidy we can now estimate changes in overall incomes from equations 9.11 and 9.14 over a range of assumptions, as shown in Table 9.2 for the years 2005/6 to 2010/11.11 Table 9.2 presents for each year the border adjusted prices estimated in one row with the demand elasticity discussed earlier (and shown in Figure 7.4) and, in another row, using analysts’ judgements. Different columns then show estimates of net benefits, benefit–cost ratios (BCRs) and fiscal efficiencies (FEs) without any growth multipliers. The main point of interest in Table 9.2 is the differences between results obtained by prices estimated using demand elasticity calculations and those (p.213) obtained by analysts’ judgements:12 estimated returns are generally higher with prices estimated using demand elasticity calculations than with those obtained from analysts’ judgements. This arises partly from lower prices in analysts’ estimates, particularly in the earlier years, due to more weight being given to the possibility of substantially lower price imports from Mozambique in 2005/6 and 2006/7 and (to a lesser extent) in 2007/8 and 2009/10.13 ## 9.5.4. Effects of growth and liquidity multipliers There is no particular methodology for the building of growth and liquidity multipliers into partial equilibrium analysis. We use equations 9.9, 9.10, 9.12, and 9.13 to estimate producers’ and consumers’ relative gains and losses, and then multiply these by relevant estimates of agricultural multipliers. As discussed earlier, a number of studies estimate agricultural multipliers of around 1.4 in sub-Saharan Africa and Malawi. We therefore initially multiply farm benefits and costs by 1.4. In order to allow for possible multiplier effects of alternative use of resources invested in the programme, we use a multiplier of 1.2 for alternative investments (the lower number to allow for the high multiplier effects of increases in income to poor rural people). Table 9.3 shows the results of this analysis together with results without the use of multipliers (also shown earlier in Table 9.2). The table shows that estimates of net benefits, benefit–cost ratios, and fiscal efficiencies generally increase when the effects of multipliers are allowed for, and these increases can be substantial. Further analysis (summarized in Table 9.4) using different multipliers for different types of people (producers, consumers, and subsidy recipients) shows that if poorer households have higher multipliers (as they normally do) and account for a higher share of national maize consumption than of national maize production, then subsidies that lead to domestic price falls will, other things being equal, generally lead to higher returns, as will greater targeting of the poor as subsidy recipients (Dorward and Chirwa, 2011b). (p.214) Table 9.3. Benefit–cost analysis without and with growth multipliers Year ED BASE Growth multiplier Net benefit BCR FE Net benefit BCR FE US$ mill

US$mill 2005/6 0.51 12.4 1.17 0.34 23.0 1.24 0.63 AE -7.6 0.90 -0.21 -3.7 0.95 -0.10 2006/7 0.51 47.8 1.49 0.65 77.5 1.61 1.05 AE 6.0 1.06 0.08 14.7 1.15 0.20 2007/8 0.51 39.4 1.30 0.41 71.6 1.42 0.75 AE 8.9 1.07 0.09 22.7 1.17 0.24 2008/9 0.51 -39.0 0.87 -0.16 -9.8 0.97 -0.04 AE -40.2 0.87 -0.16 -9.2 0.97 -0.04 2009/10 0.51 31.9 1.18 0.23 69.1 1.31 0.49 AE 35.4 1.20 0.25 58.8 1.34 0.42 2010/11 0.51 127.9 1.55 0.88 204.5 1.69 1.41 AE 106.0 1.46 0.73 134.8 1.58 0.93 Notes: ED represents demand elasticities. BCR (benefit–cost ratio) is calculated as total economic benefit divided by total economic costs. FE (Fiscal Efficiency) is calculated as net benefit (total economic benefit less total economic costs) divided by total fiscal costs. Under ED , ‘AE’ stands for Analyst Estimates as used in BCA reported in Dorward et al., (2010a); School of Oriental and African Studies et al., (2008). AE multiplier estimates derived from multiplier effects on base estimates with ED = 0.51. Economic costs exclude costs of displaced fertilizers. Data from Dorward et al., (2010a); School of Oriental and African Studies et al., (2008) and Table 9.2. Table 9.4. Alternative estimates of returns to FISP investments, 2005/6–10/11 Estimation ED Annual return Annualized return over 10 months Net benefit US$ mill

BCR

FE

AIRR

FE

Basic estimate

0.51

36.72

1.26

0.39

1.32

0.49

AE

18.09

1.09

0.13

1.11

0.16

Simple multiplier

0.51

46.30

1.31

0.58

1.39

0.73

AE

16.65

1.12

0.14

1.14

0.17

Differentiated multipliers (a)

0.51

36.56

1.34

0.60

1.42

0.76

AE

11.45

1.13

0.19

1.16

0.23

Differentiated multipliers (b)

0.51

63.41

1.44

0.84

1.55

1.07

AE

27.86

1.22

0.30

1.26

0.37

See notes on previous tables. Simple (unweighted) averages. Differentiated multipliers with consumer multiplier of 1.4, producer multiplier of 1.2, and recipient multiplier of 1.1 (a) or 1.4 (b). Annualized return if BCR is achieved over 10 months.

(p.215)

## 9.5.5. Sensitivity of BCA estimates to time of return, yields, and displacement

It was noted earlier that the use of benefit–cost ratios implies an annual return on investment. However, it might be argued that returns are achieved over a shorter period, for example 7 months from fertilizer purchase and application to harvest. This can lead to substantial increases in the Annual Internal Rate of Return (AIRR), depending on the BCR—for a BCR of 1.2 the AIRR would increase by 14% to just under 1.4, while for a BCR of 1.3 the AIRR would increase by 21% to just under 1.6. Allowance for returns over 10 months (as illustrated in Table 9.4) gives smaller increases in BCR.

For a given initial ‘without subsidy’ situation, returns to investment are also affected by changes in yield and displacement effects with the subsidy. Higher yields lead to higher returns from increased volumes of incremental production, but they also tend to lead to lower prices—increasing returns to consumers and losses to producers. The latter effect becomes important where differential multipliers are used. Where prices are very high and remain above import parity price then there are no price effects.

Increased displacement reduces incremental production, with opposite effects to those discussed above with increasing yields. Reduced returns are, however, counteracted to some extent by reduced costs, and this means that the BCR falls less than the Fiscal Efficiency (indeed if costs fall by a smaller proportion than benefits then the BCR may rise slightly while the FE falls significantly). Dorward and Chirwa (2011b) provide more detailed information on the sensitivity of investment returns to these changes.

# 9.6. Summary

We conclude with a brief summary and review of the findings in this chapter and discuss their wider relevance to the economic viability, design, implementation, and evaluation of the Malawi FISP and other subsidy programmes.

## 9.6.1. Review of findings

This chapter has considered purposes, principles, and alternative BCA methodologies against particular theoretical, methodological, and data challenges faced in BCA of the FISP. We have then put forward a formal methodology for improving the estimation of producer and consumer gains and losses and used this to provide alternative estimates of the programmes’ annual net benefit, benefit–cost ratio, and fiscal efficiency from 2005/6 to 2009/10, with further investigation of the effects of multipliers (from growth linkages and (p.216) liquidity benefits for poor households). The results (using a simple average over the five years) are summarized in Table 9.4.

Without consideration of any growth multipliers, the estimated average BCR of the six years of the subsidy programme ranges from 1.09 (the estimates using analysts’ estimates of prices) to 1.26 (with formal estimation of demand and an elasticity of demand of 0.51). Adding in multipliers raises the estimated BCRs to between 1.12 and 1.22, using analysts’ price estimates, and between 1.31 and 1.44 with more formal demand estimation. Further allowance for returns over 10 months raises the range of the AIRR to between 1.14 and 1.55 (with multipliers). These are high estimated returns and suggest that returns estimated using simple partial equilibrium analysis are downwardly biased by, in particular, exclusion of the effects of growth multipliers.

However, precise estimation of the BCR remains difficult, for reasons that are set out in this and previous chapters. Nevertheless, leaving aside the possibility of achieving returns in less than a year, and taking formal price estimation as more reliable than analysts’ estimation, suggests that the average BCR is likely to be around 1.35 after allowing for the effects of multipliers, with fiscal efficiency of around 0.6. Lower estimates using analysts’ price estimates give an estimated BCR of around 1.15 and fiscal efficiency of 0.2. These estimates are sensitive to yield responses (and hence both programme implementation and weather), and international maize prices. The latter have been higher in recent years, and are likely to remain high, and there is considerable potential for higher yield responses than those assumed here. Higher displacement would not affect the BCR very much but would lower fiscal efficiency.

## 9.6.2. Economic viability of the Malawi FISP

Overall these returns are high and suggest that the FISP has provided a good return on investment—with scope for improved efficiency and effectiveness to make returns much higher in the future. However there are, of course, also risks of poor implementation, unfavourable weather, and changes in prices that depress returns.

The extent to which the FISP represents the best use of investment funds depends upon competition for funds between different investments and their relative returns. Buffie and Atolia (2009) find, using CGE analysis, the net benefits of the FISP depend critically upon the relative returns to fertilizer use and to investments in roads, and upon the extent to which investment in FISP crowds out investments in infrastructure. They conclude that a strategy of mixed investments is probably best. However Filipski and Taylor (2011) find that CGE model results are sensitive to model formulation regarding seasonal finance constraints on input purchases—which were not allowed for (p.217) by Buffie and Atolia. Fan et al. (2007) report that investments in education, roads, agricultural research and development, credit subsidies, and input subsidies (in that order) all yielded high returns in such a mixed investment strategy in the early stages of the Green Revolution in India.14

There is very limited specific information on returns to alternative investments, such as in roads and in agricultural research and development in Malawi, and it is common to rely on estimates from other African countries or from Asia. These tend to show very high returns to these investments. Buffie and Atolia (2009) use returns to infrastructure investment of between 10 and 30% (a BCR of 1.1 to 1.3), citing evidence from Fan et al. (2003) and Pohl and Mihaljek (1992). Alston et al. (2000) report a modal rate of return of 43% to agricultural research from a meta-analysis of studies but report very wide ranges in estimates with some possible biases indicated by lower estimates in peer reviewed and ex ante (as opposed to ex post) studies and in studies in LDCs. Estimated returns from the FISP are comparable with these estimates. None of these returns allow for wider impacts, such as the health and education benefits discussed in Chapters 6 and 7 and the long-run effects of reduced food shortages and malnutrition on children’s mental and physical development and subsequent adult productivity. Any such allowance would have to take into account likely differences across the different investments being compared, as other investments may also yield such benefits without including them in the estimation of returns to investment.

## 9.6.3. Implications for subsidy programme design and implementation

The formal price analysis and introduction of multipliers in the BCA in this chapter reinforces previous studies’ discussions of the lessons from BCA for FISP and other subsidy programme design and implementation: returns will be improved by measures that increase yield responses to fertilizer (for example, earlier input delivery, greater emphasis on integrated soil fertility management, improved application, more cost effective formulations, more technical advice, more targeting to the poor) and that reduce displacement (for example, better regional and household targeting, better control of diversion and fraud, earlier registration and input delivery). The inclusion of multipliers in the BCA strengthens the importance of all of these issues, as gains from improved efficiency and effectiveness are multiplied. It also adds further weight to the importance of targeting, of ensuring that maize marketing (p.218) policies allow increased maize production to lower maize prices (as benefits to poorer subsidy recipients and consumers tend to have higher multipliers) and suggests that to maximize linkages and reduce leakages (Dorward et al., 2003) there should be complementary investments in measures facilitating the growth of the non-farm economy and of non-staple agriculture (for example, horticulture, legumes, and livestock) in response to subsidy-led growth real in real incomes.

## 9.6.4. Implications for future data collection and benefit–cost analysis

The partial equilibrium methods developed in this chapter have sought to follow and find appropriate compromises between the seven principles set out in Section 9.2: being practicable, externally consistent, contextualized, holistic, internally consistent, transparent, and cost-effective. The method is relatively simple in terms of its data needs and the calculations required but nevertheless it takes account of the context and complex processes affecting FISP returns, and it also addresses the key questions that policy makers and technicians ask (regarding both FISP’s overall returns—for comparison with other investments—and the critical variables that determine its effectiveness and efficiency). It could be improved by further research leading to better estimates of maize price determinants and of growth multipliers, and by more robust estimation of (quite probably changing) demand elasticity for maize and better information on yield and production effects of subsidized inputs.

Its application does, therefore, highlight the need for good data in Malawi’s agricultural sector. This is a major challenge. Malawi has excellent data on market prices, and the biennial FISP evaluation surveys have provided valuable information on targeting and use of subsidized inputs. However there are continuing difficulties with data on the total number of farm households, on cropping areas and yields, and on yield responses to inputs and agronomic management. Improved data on these variables is critical not just for the evaluation of the FISP, but for much wider policy development, monitoring, and evaluation.

## Notes:

(1) This chapter draws heavily on Dorward and Chirwa (2011b).

(2) These regression models are different from those discussed earlier in Chapter 7. The models discussed there can provide insights into economy-wide impacts, but their use in capturing all the major economy-wide impacts of a programme are limited if there is substantial market integration and price transmission across different areas. This will often be the case for cereal markets within countries.

(3) We do not attempt to consider the health and education benefits discussed in Chapter 7 in the benefit–cost analysis in this chapter. In using market prices as the basis of valuation we are also ignoring questions raised about the value of maize to people who cannot afford to buy it at higher prices.

(4) This section contains quite detailed consideration of methodological issues in improving BCA methods. Readers without specific technical interests in this may prefer to skip the section and go straight to Section 9.6.

(5) The 2006/7, 2008/9, and 2010/11 household surveys reported in Dorward et al. (2010a) and School of Oriental and African Studies et al. (2008) show that almost all the incremental fertilizer use as a result of the subsidy programme was applied to maize and there is no evidence of shifts in cropping patterns in 2008/9 as a result of the subsidy programme. (Holden and Lunduka (2010c) also find no evidence of shifts in cropping patterns, although Chibwana et al. (2012) suggest some shifting into maize by subsidy recipients.)

(6) The assumption of autarchy is a reasonable analytical starting point for the Malawi maize market, given the high transport costs in exporting to or importing from the world market. We consider later the effects of informal imports from surrounding countries (notably Mozambique), actual or potential price ceilings from potential imports from South Africa, and exports to Zimbabwe in 2007/8.

(7) In the long run the loss of producer incomes from falls in unsubsidized maize production and in prices may be smaller than estimated here as rising real incomes for consumers will raise prices for non-maize and non-farm goods and services, which can replace their lost and/or lower value maize production.

(8) Note that where producers outside an economy export into that economy but at prices largely determined within the economy (as is broadly the case with Mozambican exports to Malawi), then the loss of producer income suffered by these producers due to the price fall is not a loss to the domestic producers and the domestic economy.

(9) Restriction of the data series to the 1993/4 to 2005/6 seasons (a) provides more consistent estimates than are obtained from the 1993/4 to 2009/10 series and (b) standardizes for the effects of possible inconsistency in production estimates and of higher nominal wages in later years.

(10) See School of Oriental and African Studies et al. (2008) for summary of a range of different studies from which these estimates were derived.

(11) Elasticities of demand per se were not used in these calculations, due to averaging problems over price and quantity ranges; instead the estimated equations were used to calculate price and quantity changes.

(12) Differences in results across different years are due to variation in maize prices (with high domestic prices from 2007/8 requiring analysis using import parity prices for the ‘without subsidy’ situation—and even for the ‘with subsidy’ situation in 2007/8), and in fertilizer prices (which rose steadily from 2005/6 to a peak in 2008/9). Differences in some results from those presented in Dorward and Chirwa (2011b) are due to allowance here for weather-affected yields, as set out in the incremental production estimates presented in Chapter 6.

(13) Where ‘without subsidy’ domestic prices would be higher than import parity, the formal price estimation also allows for part of the subsidized production to substitute for imports (so that consumer benefits are not derived from a simple average of import parity and ‘with subsidy’ domestic price).

(14) Rationing of large unit subsidies in the FISP should make it more efficient than India’s universal subsidies; and its impact on liquidity constraints in the absence of a credit programme should mean that it generates some of the benefits that Fan et al. report for credit subsidies in India. Fan et al.’s estimates of returns to subsidies relative to roads may be under-estimated to some extent as a result of higher cross-region spillover effects from subsidies, not captured in the model.