Smart Subsidy? Welfare and Distributional Implications of Malawi’s FISP
Hanan Jacoby1
ABSTRACT
It is often argued that subsidizing fertilizer and other inputs is desirable both to boost agricultural
production and to help poor farmers. This analysis of Malawi’s huge Farmer Input Subsidy Program
highlights a tension between these two objectives: The more FISP increases fertilizer use and thereby
raises output, the greater the distortion and hence the lower the welfare gains from the program.
Indeed, the empirical results indicate that up to 59% of every Kwacha spent on the FISP is wasted, in the
sense that the fertilizer is not sufficiently valued by the beneficiaries. Cashing out the program is shown
to have desirable distributional implications.
1
DECAR, World Bank. This note was prepared as background for the AFR regional study entitled Options for
Improving Agriculture Public Expenditures in Africa (funded by the Africa Chief Economists Office and the Gates
Foundation) led by Aparajita Goyal and John Nash. I am grateful to them for helpful suggestions as well as to
Sinafikeh Gemessa for able research assistance.
Malawi’s Farmer Input Subsidy Program or FISP is undoubtedly the largest such scheme relative to GDP
in sub-Saharan Africa. Perhaps as a result it has become something of a cause célèbre (e.g., Denning et
al. 2009). What sets FISP apart is its vast coverage—around 1.4 million (44% of) agricultural households
by 2012/13—combined with its use of vouchers to target subsidies to poor farmers, a so-called “smart”
subsidy. Since FISP alone accounts for around 9% of Malawi’s government budget, it is important to
understand its welfare and distributional implications.
To do so, the analysis described in this note hews closely to the welfare economics tradition. That is, it
assumes, at least as a starting point, that demand reflects marginal valuation and thus can be used to
measure the benefits (and costs) of policy interventions. The empirical application, therefore, involves
first estimating a demand curve for fertilizer using micro-data and then simulating “consumer surplus”
changes implied by the smart subsidy scheme. In an extension, the possibility that credit constraints
distort fertilizer use decisions is taken seriously. In this case, demand may understate marginal
valuation. Nonetheless, the analysis can be adapted to ‘adjust’ demand for the presence of credit
constraints and recover the true benefits of fertilizer subsidies.
Conceptual framework
Smart ISPs typically provide farmers with vouchers to purchase small quantities of fertilizers and seeds.
The quantity limitation, often combined with explicit targeting of vouchers, is designed to reduce the
share of benefits going to larger, wealthier, farmers for whom the subsidy is likely to be inframarginal.
Insofar as the subsidy is not inframarginal, thereby changing the quantity of fertilizer procured, the
critical question is: What is a voucher worth to farmers? If vouchers can be costlessly resold at the
market price, then a voucher is, of course, equivalent to a cash grant of the subsidy amount. Since FISP
voucher resale is rare in Malawi (Kilic et al. 2013 and more recent evidence cited below), the remainder
of this discussion presupposes that vouchers are not equivalent to cash.
Figure 1 displays four smart subsidy scenarios based on four different levels of demand for fertilizer.
Suppose that, as in FISP, a voucher is provided that can be redeemed for a single 50 kg. bag of urea (an
identical argument applies to the NPK voucher). Upon redemption, farmers must pay some fraction of
the market price ; i.e., > 0. It is also assumed, plausibly in the context of Malawi, that is given
on world markets. Thus, none of the subsidy benefits are dissipated in the form of producer surplus.
1
Taking the four scenarios in turn, case 1 shows a demand for fertilizer so low that none would be
purchased at the subsidized price even if it were possible to purchase in fractions of 50 kg bags. Case 2
shows a demand just high enough to make it worthwhile to redeem the voucher. Note that redemption
forces the farmer to purchase a whole 50 kg bag at a price of , even though in this case the farmer
would want to purchase only a fraction of a bag. The net welfare gain to the farmer from the subsidy is
represented by the area of the solid blue triangle minus the area of the solid red triangle. As in case 2,
in case 3 the subsidy induces the farmer to procure more fertilizer than he otherwise would. However,
the marginal value of these additional units to the farmer is less than the cost of providing them. This
difference is represented by the dotted blue triangle in Figure 1. Lastly there is the purely inframarginal
subsidy, represented by case 4. Here, the subsidy does not change farmer behavior at all and, as a
consequence, the welfare gain, the entire blue rectangle, is equal to the cost of the subsidy. In other
words, case 4 is the only situation where the subsidy benefits the farmer and does not entail a
deadweight loss.
Thus far, the analysis takes the stand that demand reflects marginal value. But what if farmers are
constrained from making optimal input use decisions? For example, by lack of credit. Returning to case
′
3, suppose that unconstrained demand is 3 as illustrated in Figure 2. While the constrained demand
3 indicates how much quantity of fertilizer procured would increase in response to the subsidy, it
would, in general, understate the welfare gain from this quantity increase. For an unconstrained
farmer, the value of additional fertilizer use is given precisely by the value of the additional crop it
produces. But for a credit constrained farmer, the value of additional fertilizer also depends on the
shadow price of transferring resources from the present to the future. In other words, credit constraints
′
raise the shadow price of fertilizer at any given value of the monetary price.2 Thus, 3 reflects the true
productivity benefits of an increase in fertilizer use and, correspondingly, the solid blue area in Figure 2
represents the additional benefit to the household (i.e., above and beyond that reflected by 3) from a
non-inframarginal subsidy.
2
This can be seen most easily in a model where households have preferences over a single consumption good in
both a pre and post-harvest period. Given that post-harvest consumption is always greater than pre-harvest
consumption, the shadow price of fertilizer, which must be purchased before harvest, always exceeds the
monetary price.
2
Empirical framework
The empirical model is described by three equations (see technical appendix for details): (i) a demand
curve for each type fertilizer relating quantity procured to the effective price; (ii) a price equation
relating per unit effective price to distance to fertilizer source;3 (iii) a voucher redemption equation. A
combination of equations (i) and (ii) is estimated on a sample of households that do not receive fertilizer
vouchers and equation (iii) is estimated on a sample of voucher recipients.
The key problem the model is designed to solve is the lack of good data on commercial fertilizer prices
faced by each household. Even if such data were available, including for households that choose not to
purchase any fertilizer and for communities where no fertilizer is sold, the exogeneity of prices would be
an issue. To work around this lacuna, the analysis uses distance between household and source of
fertilizer (i.e., fertilizer plant or port of entry into Malawi), which is plausibly exogenous and available for
every household whether purchaser or not. However, absent direct information of prices, the price
elasticity or slope of the demand is not identified from equations (i) and (ii) alone. Since without this
demand elasticity it is impossible to do welfare analysis, an auxiliary relationship between voucher
uptake and household characteristics is required; hence equation (iii). The technical appendix describes
how all three equations fit together to identify the price elasticity of demand.
Finally, note that credit or cash-in-hand constraints are incorporated in the model by including a
measure of household income (in practice, per capita expenditures) in the fertilizer demand equation (i).
In the absence of credit constraints, fertilizer use should be unrelated to income, conditional on prices
and productivity.4
Data and preliminary analysis
Data come from Malawi’s 2013 ISA survey, a nationally representative survey that includes information
on FISP voucher receipt and redemption. In addition, GPS coordinates are available for all dwellings of
the roughly 4000 surveyed households, allowing construction of the appropriate distance variables.
3
Effective price means the relative price of a kg of fertilizer in terms of a kg of, say, maize at the farm-gate.
4
Strictly speaking, separability between production and consumption decisions also requires a complete set of
factor markets as well as, in the presence of uncertainty, complete contingent claims markets.
3
Table 1 provides descriptive statistics on fertilizer voucher receipt and redemption in the ISA sample.
On the whole, households receiving vouchers used them, but around 10% of recipients nationally did
not redeem at least one voucher. Only a handful, however, reported selling the voucher.
Demand estimation
Table 2 presents tobit estimates of the relationship between fertilizer use (separately for NPK and urea)
and household characteristics, including most importantly log distance of household from fertilizer
source (nearest of fertilizer plant or port of entry into Malawi) and log per capita expenditures. The
regressions also control for household demographics, landholdings, indicators of soil productivity based
on the household’s GIS coordinates, and district dummies.5 In addition, to deal with the concern that
log per capita expenditures is endogenous with respect to household fertilizer purchase, this covariate is
instrumented with the leave-one-out mean of log per capita expenditures in the enumeration area.
Note that the distance coefficients are negative and per capita expenditure coefficients are positive for
both fertilizer types. Thus fertilizer use of voucher non-recipient households declines with distance to
the production point or port of entry for this input. And, wealthier households purchase more fertilizer,
conditional on soil productivity, which is consistent with a model of cash-on-hand constraints (see Duflo
et al., 2011). These demand estimates along with the probit estimates for voucher redemption on the
sample of voucher recipients (not reported), provide estimates of the underlying demand parameters as
discussed in the technical appendix.6
Smart subsidy?
Consumer surplus is computed for each household based on their predicted demand for the two types
of fertilizer under the smart subsidy scheme relative to the counterfactual of commercial purchase.
Table 3 breaks down voucher recipient households into the four cases discussed in reference to Figure 1.
Only a few households are predicted to be in the inframarginal category (case 4). Most are predicted to
5
The large set of controls is a way of addressing possible selection bias due to the fact that voucher non-recipients
are not randomly chosen.
6
Following the notation in the technical appendix, this procedure yields = −.174 and = −.099.
4
purchase less than one bag commercially in the absence of the subsidy; hence, for them FISP increases
the quantity of fertilizer acquired.
If one takes consumer surplus, summed across fertilizer types, as a measure of the benefit of FISP and
the difference between the effective price (i.e., inclusive of transport costs)7 and the subsidized price
(times the number of vouchers redeemed) as the cost of FISP, then a benefit to cost ratio can be
computed, for both the overall population and for different sub-populations. The results of this exercise
are reported in Table 4.
Recall that consumer surplus can be computed in two ways: First, by assuming that each household’s
actual or ‘constrained’ demand schedule reflects their marginal valuation of fertilizer; second, by
assuming that the household’s marginal valuation is represented by their demand ‘as if’ they did not
face a binding cash constraint. ‘Unconstrained’ demand in Table 4 uses household fertilizer demand
evaluated at the 90th percentile of per capita consumption (rather than at actual household per capita
consumption); farmers in the top 10% of the wealth distribution are unlikely to be cash constrained in
their purchase of fertilizer.
The key finding is that benefit cost ratios are well below 1, the upper bound achieved when all
households are inframarginal with respect to the FISP. For consumer surplus computed based on
constrained demand, the national benefit/cost ratio is only 0.41, which means that 59% of every Kwacha
spent on FISP is wasted. The poor account for much more of this deadweight loss than the non-poor for
the simple reason that the poor have a lower demand for fertilizer. If consumer surplus is computed
based on unconstrained demand, however, the national benefit/cost ratio rises to 0.62, a significant
improvement, but still indicative of a highly inefficient transfer (relative to cash). Obviously, moving
from constrained to unconstrained demand as a basis for computing consumer surplus attenuates the
difference in benefit/cost ratios between poor and non-poor.
As a final step, figures 3 and 4 show benefit incidence curves for FISP. In each figure, the naïve BIC is
plotted, which is just the share of vouchers going to the bottom kth percentile of the per capita
expenditure distribution. Evidently, FISP voucher distribution does not target the poor particularly well;
indeed, there is no discernable progressivity in the distribution of vouchers. However, when the actual
benefit (consumer surplus) due to the voucher is taken into account, FISP appears much more
7
FISP reduces the effective price in two ways: by fixing a low pan-territorial subsidized price and by actually
delivering fertilizer to local shops for sale at this price, which, of course, entails a sizeable transport cost.
5
regressive, which again is attributable to the low demand for fertilizer among the poor. Using the more
generous (to FISP) definition of consumer surplus, in figure 4, improves progressivity, but the program
remains more regressive than the naïve BIC would suggest.
Conclusions and policy implications
It is often argued that subsidizing fertilizer is desirable both to boost agricultural production and to help
poor farmers. The lesson here is that there is a tension between these two objectives: The more FISP
increases fertilizer use and thereby raises output (i.e., the less crowd-out), the greater the distortion and
hence the lower the welfare gains from the program. Indeed, the results of this analysis of Malawi’s
FISP suggest that the magnitude of this distortion is high. Up to 59% of every Kwacha spent on the FISP
is wasted, in the sense that the fertilizer is not sufficiently valued by the beneficiaries. Even in the
rosiest scenario considered, the estimates indicate that 38% of FISP expenditures are deadweight loss.
Allocating the FISP budget through a targeted cash transfer program avoids these welfare costs and
would still stimulate the demand for fertilizer among smallholders in Malawi to some extent; i.e., by
alleviating the credit constraint. The predicted distributional impact of such a program ‘cash-out’ under
different assumptions about fertilizer demand (i.e., constrained versus unconstrained) are illustrated in
figure 5.8 In either case, a cash-out is evidently a highly progressive policy change, in absolute terms
benefitting households in the bottom quintile far more than households in the top quintile.
References
Denning, G., Kabambe, P., Sanchez, P., Malik, A., Flor, R., Harawa, R., ... & Sachs, J. (2009). Input
subsidies to improve smallholder maize productivity in Malawi: Toward an African Green Revolution.
PLoS Biol, 7(1), e1000023.
Duflo, E., Kremer, M., & Robinson, J. (2011). Nudging Farmers to Use Fertilizer: Theory and
Experimental Evidence from Kenya. American Economic Review, 101(6), 2350-90.
Kilic, T., Whitney, E., & Winters, P. (2013). Decentralized beneficiary targeting in large-scale development
programs: insights from the Malawi farm input subsidy program. World Bank Policy Research Working
Paper, (6713).
8
The policy simulations assume that the cash transfer would include the value of the costs otherwise incurred by
the program in transporting the fertilizer to beneficiaries.
6
Technical Appendix
∗
The demand for fertilizer type j for farmer i is assumed to take the form
∗
ln( + 1) = + + (1)
where is the farm-gate price of fertilizer in real terms (i.e., in terms of crop output). The parameter
is the intercept, which can depend on farmer characteristics (e.g., land holdings), and < 0 is the
price-elasticity of demand for fertilizer j. In what follows, the j subscript is suppressed for convenience.
The farm-gate price depends on cost of transport from port/production source. Thus, is a function of
market price at source, , and the distance to source as follows
= + ln( ) + (2)
where > 0 is a parameter to be estimated .
Combining (1) and (2) yields
ln(∗ + 1) = ′ + ′ ln( ) + ′ (3)
where ′ = + , ′ = , and ′ = + . Equation (3) can be estimated by tobit to account
for censoring at zero.
Next, consider the decision to redeem vouchers by voucher recipients. The price they face for a 50 kg
bag is assumed to be
= (1 − s) +
where s is the subsidy rate. Note that, since Malawi effectively has pan-territorial pricing of subsidized
fertilizer, the cash price of fertilizer purchased with a voucher is the same at every location up to
random noise (i.e., think of this as a ‘hassle’ cost). This delivers a probability of voucher redemption
of the form
Pr(redeem) = Pr[ ̂ ′ ,
̃ ( ∝ ̂ ′ /)> , ]
′ ̂′
= Pr[ < ̂ , /) − (1 − s) ]
̃ ( ∝
̃ is the take-it-or-leave-it price of a 50 kg bag. Equation (1) implies that
where ̃ = − ( + 1 −
51 1 51 ′
∗ 51)/ = − , where = ̂ ′ [1 − 50 ∗
̂ ]. From this it follows that
51+∝
50
− −(1−s) −
Pr(redeem) = Φ [
]=Φ [
]
where Φ is the standard normal CDF and is the standard deviation. Thus, the slope coefficient from
this voucher redemption probit identifies -/ and the constant term identifies s /. Since s is a
known constant, both and follow directly, as does and, finally, .
7
Figure 1. Four smart subsidy scenarios
Figure 2. Additional welfare gains based on unconstrained demand
8
100
80
60
40
20
0
0 20 40 60 80 100
Percentile of real annual expenditure on food and non-durable goods per capita
Fertilizer voucher share Consumer surplus share
Figure 3. Benefit incidence based on constrained demand (ag. households)
100
Benefit incidence curves with
unconstrained demand for agricultural
80
households
60
40
20
0
0 20 40 60 80 100
Percentile of real annual expenditure on food and non-durable goods per capita
Fertilizer voucher share Consumer surplus share
Figure 4. Benefit incidence based on unconstrained demand (ag. households)
9
Figure 5. Benefit distribution of a FISP cash-out
Table 1: Number of households receiving and redeeming vouchers in Malawi ISA 2013
North Central South National
NPK Urea NPK Urea NPK Urea NPK Urea
Voucher recipients 246 244 315 348 512 489 1073 1081
Full redeemers 236 234 268 295 465 432 969 961
Non-redeemer 5 7 32 46 36 47 73 100
Partial or non-redeemers 10 10 47 53 47 57 104 120
Of whom, no. who sold 1 4 4 5 3 3 8 12
10
Table 2: Tobit estimates of demand for commercial fertilizer for non-recipients of vouchers
Variables Log (kg NPK + 1) Log (kg urea +1)
Log(km from HH to nearest main border port -0.931 -0.722
or local fertilizer plant) (2.71)** (2.21)*
log(annual HH per capita consumption) 2.350 2.122
(6.46)** (6.00)**
log (ha cultivated by HH) 0.442 0.408
(4.28)** (4.06)**
Household size (adult equivalent) 0.391 0.421
(7.02)** (7.82)**
Female headed HH (=1) -0.536 -0.586
(2.10)* (2.40)*
Age of household HH head -0.028 -0.023
(3.84)** (3.26)**
Plot conditions
Workable soil (=1) -0.211 0.169
(0.37) (0.31)
Non-toxic soil (=1) -0.525 -0.500
(0.61) (0.63)
Oxygen available to crop roots (=1) 0.337 -0.398
(0.61) (0.78)
Good rooting condition (=1) -0.245 -0.304
(0.49) (0.64)
Good soil nutrient retention capacity (=1) 0.248 0.808
(0.44) (1.50)
Good soil nutrient availability (=1) -1.058 -0.860
(1.96)* (1.67)
Average elevation (meters) 0.004 0.003
(5.26)** (4.34)**
1st stage residual -0.245 -0.297
(0.64) (0.79)
Observations 1700 1700
Notes: Absolute value of t statistics in parentheses (* significant at 5%; ** significant at 1%). District
dummies included but not reported. Log per capita consumption is assumed to be an endogenous
variable. Thus, the residual from a first-stage regression of log per capita consumption on (leave-one-
out) mean of log per capita consumption for the enumeration area and the other exogenous variables is
included in the tobit specifications.
11
Table 3: Number of households in each demand category based on predicted demand
Cases (see figure 1) NPK Urea
1 : no demand at 9 7
2 : marginal willingness to pay for one bag < 267 242
3 : > marginal willingness to pay for one bag > 776 809
4 : marginal willingness to pay for one bag > (inframarginal) 13 17
Total 1065 1075
Table 4: Benefit/Cost ratios for FISP
Constrained Unconstrained
demand demand
Region All Ag. households
North 0.65 0.78
Central 0.52 0.68
South 0.26 0.54
National 0.41 0.62
Poor Ag. households
North 0.55 0.74
Central 0.37 0.61
South 0.14 0.41
National 0.29 0.53
Non-poor Ag. households
North 0.71 0.81
Central 0.59 0.71
South 0.31 0.60
National 0.46 0.66
Notes: See text for details. Unconstrained demand assumes
all households value fertilizer as though they were in the 90th
percentile of the per-capita expenditure distribution.
12