Nudging Farmers to Use Fertilizer: Theory and Experimental Evidence from Kenya

Abstract

While many developing-country policymakers see heax'y fertilizer subsidies as critical to raismg agricultural productivity, most economists see them as distortionary, regressive, environmentally unsound, and argue that they result in politicized, inefficient distribution of fertilizer supply. We model farmers as facing small fixed costs of purchasing fertilizer, and assume some are stochastically present-biased and not fully sophisticated about this bias.Even when relatively patient, such fanners may procrastinate, postponing fertilizer purchases until later periods, when they may be too impatient to purchase fertilizer. Consistent with the model, many farmers in Western Kenya fail to take advantage of apparently profitable fertilizer investments, but they do invest in response to small, time-limited discounts on the cost of acquiring fertilizer (free delivery) just after har\'est. Later discounts have a smaller impact, and when given a choice of price schedules, many farmers choose schedules that induce advance purchase. Calibration suggests such small, time-limited discounts yield higher welfare than either laissez faire or heavy subsidies by helping present-biased fanners commit to fertilizer use without inducing those with standard preferences to substantially overuse fertilizer. ' The authors are respectively from MIT (Department of between future periods). In each period /.-, with some probability p, the fanner is fairly patient (/3i. = pfi), and with probability ( 1 -p), the fanner is quite impatient {6k = Pl).Furthermore, while fanners do recognize that there is a chance that they will be impatient in the future, they overestimate the probability that they will be patient. Specifically, the probability that a patient farmer believes that she will still be patient in the future is p > p.There are several ways to interpret this stochastic rate of discount. One interpretation is that farmers are literally partially naive about their hyperbolic discounting, as in the original O'Donoghue and Rabin (1999) Define the incremental yield to fertilizer as jWe assume that the cost of reselling fertilizer is sufficiently large to discourage even (1)>y (2) .': (4 •'Rearranging, we find that the farmer will wait ifWhen p = 0, the right hand side is equal to /3//(y(l) -1). If we assume that the utilir\' cost of using fertilizer is small enough that /?//(y(l) -1) is larger than / + -~-^, then the right 10 hand side of the inequality is larger than the left hand side. For the remainder of the model, we assume that p > p*{R). Note that since impatient period 1 fanners will not save in any case, it is not necessan,' that they believe they will be more patient in the future than they are in the present for this procrastination problem to arise.Instead, it is only necessary that patient farmers overestimate the probability that they will continue to be patient in the fuaire. This tendency to believe that future tastes will more closely resemble current tastes than they actually will, termed "projection bias," has found c...

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