Cognitive droughts

The intervention is the random assignment (at no cost to the recipient) of rainfall insurance, which pays out a lump sum of R$ 170 (about USD 60) by the end of June if the municipal-level harvest loss is 70% or above, according to State's extension authority report publicized by May 31st, 2015.

2015-03-09

2015-06-20

We document the effects of our treatments on 5 types of outcomes:

(1) Economic decisions related to water, e.g.: real decisions, from the accuracy of farmer's recall of the number of rainy within the last 30 days to the accuracy of their estimate of the volume of water in their water tanks; and decisions in hypothetical experiments, including patience, trust and reciprocity in water-related tasks;

(2) Economic decisions unrelated to water, e.g.: decisions in hypothetical experiments, including patience, trust and reciprocity in non-water related tasks;

(3) Cognitive performance in tasks related to water, e.g.: sensitivity to framing and attention and memory in water-related tests;

(4) Cognitive performance in tasks unrelated to water, e.g.: sensitivity to framing and attention and memory in non-water related tests;

(5) Other outcomes, e.g. locus of control

We have several outcome variables for each of the 5 types of outcomes. Whenever we have matching questions for types (1) and (2) - e.g. the same experiment about patience, related to water in one case, and unrelated in the other case - or (3) or (4) - e.g. the same experiment about attention, related to water in one case, and unrelated in the other case -, we also consider a derivative outcome given by the difference between the two outcomes.

For cognitive outcomes, we consider two versions of each: penalized by response time over the phone, and not penalized.

We will include municipality fixed-effects in order to control for fixed unobservable factors, in particular different random assignment probabilities (since the number of eligible farmers in each municipality is unknown). We will cluster standard errors at the individual-level.

We will convert all outcomes to z-scores and take the average of them within each type, using those averages as dependent variables besides analyzing each outcome in isolation.

When farmers start making production-related decisions, but before uncertainty is resolved – in early March –, we will provide two randomly assigned treatments. First, we will enroll 1,000 farmers in Government-subsidized insurance (Treatment 1). Second, half our subjects will be randomly assigned to a drought-related message at the begging of each automated voice call (interactive voice response unit, IVR) through which we run the survey (Treatment 2), while the others will listen to neutral message.

We expect the drought-related message to prime farmers about water scarcity, making water top-of-mind with a higher likelihood for uninsured farmers. In principle, insurance should shield farmers’ psychology from the scarcity environment (at least partially).

Table 1 – Experimental design

Insured Not insured
Neutral message Treatment 1 Control group
Drought message Treatment 1 x Treatment 2 Treatment 2

Randomization done in office by a computer

Individual

No

2,000 to 5,000 farmers

8,000 to 20,000 (2,000 to 5,000 farmers over 4 waves)

1,000 farmers in the treatment group, and up to 4,000 farmers in the control group

Power Calculations Power calculations for some outcomes of interest are based on the results of the June wave of the 2014 pilot. Calculations of minimum detectable effects assume 10%, 5% or 1% statistical significance, 80% statistical power, a sample size of 5,000 farmers, 50% of non-response rate (also based on the average for the 2014 pilot) and 50% random assignment to priming about rainfall (a crucial element of the experiments). Given these parameters, minimum detectable effects (in absolute value) are given by: |MDE|=(t_(1-κ)+t_alpha ) √(σ^2/p(1-p) x 4/NxW) , Where t_(1-κ) is the t-statistic associated with confidence level 1-κ, t_α is the t-statistic associated with power α, σ is the standard deviation of the effect, p is the proportion of the 5, observations in the treatment group, N is the number of observations, and W is the number of waves. The term 4/NxW incorporates the 50% non-response rate and the 50% random assignment to priming about rainfall, which divide the effective number of observations by a factor of 4. Tables 1 to 3 present computations for the outcomes that most resemble the ones we would like to include the 2015 design, under 10%, 5% and 1% significance levels. Table 4 presents the details of the computations for one of the outcomes as an example. Table 1 – Minimum detectable effects (absolute value) under 10% significance (A) Two waves Minimum Detectable Effect (absolute value) June coefficient June std. dev. Average T = 1250 T = 1125 T = 1000 T = 875 T = 750 T = 625 T = 500 T = 375 T = 250 Cognitive tasks Digit span 0.13 0.09 0.24 0.035 0.036 0.038 0.040 0.042 0.046 0.050 0.057 0.069 Stroop 0.01 0.08 0.19 0.032 0.033 0.034 0.036 0.038 0.041 0.046 0.052 0.063 Garbled words 0.06 0.13 0.18 0.041 0.043 0.045 0.047 0.050 0.054 0.060 0.068 0.082 Price recall Beans (Week 1) -0.11 0.11 0.31 0.038 0.039 0.041 0.043 0.046 0.049 0.054 0.062 0.075 Corn (Week 1) -0.08 0.11 0.29 0.039 0.040 0.042 0.044 0.047 0.050 0.056 0.063 0.077 Goat (Week 1) 0.02 0.08 0.16 0.033 0.034 0.035 0.037 0.040 0.043 0.047 0.054 0.065 (B) Five waves Minimum Detectable Effect (absolute value) June coefficient June std. dev. Average T = 1250 T = 1125 T = 1000 T = 875 T = 750 T = 625 T = 500 T = 375 T = 250 Cognitive tasks Digit span 0.13 0.09 0.24 0.022 0.023 0.024 0.025 0.027 0.029 0.032 0.036 0.044 Stroop 0.01 0.08 0.19 0.020 0.021 0.022 0.023 0.024 0.026 0.029 0.033 0.040 Garbled words 0.06 0.13 0.18 0.026 0.027 0.028 0.030 0.032 0.034 0.038 0.043 0.052 Price recall Beans (Week 1) -0.11 0.11 0.31 0.024 0.025 0.026 0.027 0.029 0.031 0.034 0.039 0.047 Corn (Week 1) -0.08 0.11 0.29 0.024 0.025 0.026 0.028 0.030 0.032 0.035 0.040 0.048 Goat (Week 1) 0.02 0.08 0.16 0.021 0.021 0.022 0.024 0.025 0.027 0.030 0.034 0.041 Table 2 – Minimum detectable effects (absolute value) under 5% significance (A) Two waves Minimum Detectable Effect (absolute value) June coefficient June std. dev. Average T = 1250 T = 1125 T = 1000 T = 875 T = 750 T = 625 T = 500 T = 375 T = 250 Cognitive tasks Digit span 0.13 0.09 0.24 0.039 0.041 0.043 0.045 0.048 0.052 0.057 0.065 0.078 Stroop 0.01 0.08 0.19 0.036 0.037 0.039 0.041 0.043 0.047 0.051 0.059 0.071 Garbled words 0.06 0.13 0.18 0.047 0.048 0.050 0.053 0.057 0.061 0.067 0.077 0.093 Price recall Beans (Week 1) -0.11 0.11 0.31 0.043 0.044 0.046 0.048 0.052 0.056 0.061 0.070 0.084 Corn (Week 1) -0.08 0.11 0.29 0.043 0.045 0.047 0.050 0.053 0.057 0.063 0.071 0.086 Goat (Week 1) 0.02 0.08 0.16 0.037 0.038 0.040 0.042 0.045 0.048 0.053 0.061 0.073 (B) Five waves Minimum Detectable Effect (absolute value) June coefficient June std. dev. Average T = 1250 T = 1125 T = 1000 T = 875 T = 750 T = 625 T = 500 T = 375 T = 250 Cognitive tasks Digit span 0.13 0.09 0.24 0.025 0.026 0.027 0.028 0.030 0.033 0.036 0.041 0.049 Stroop 0.01 0.08 0.19 0.023 0.023 0.024 0.026 0.027 0.030 0.033 0.037 0.045 Garbled words 0.06 0.13 0.18 0.029 0.031 0.032 0.034 0.036 0.039 0.043 0.048 0.059 Price recall Beans (Week 1) -0.11 0.11 0.31 0.027 0.028 0.029 0.031 0.033 0.035 0.039 0.044 0.053 Corn (Week 1) -0.08 0.11 0.29 0.027 0.029 0.030 0.031 0.033 0.036 0.040 0.045 0.055 Goat (Week 1) 0.02 0.08 0.16 0.023 0.024 0.025 0.027 0.028 0.030 0.034 0.038 0.046 Table 3 – Minimum detectable effects (absolute value) under 1% significance (A) Two waves Minimum Detectable Effect (absolute value) June coefficient June std. dev. Average T = 1250 T = 1125 T = 1000 T = 875 T = 750 T = 625 T = 500 T = 375 T = 250 Cognitive tasks Digit span 0.13 0.09 0.24 0.048 0.050 0.052 0.055 0.058 0.063 0.069 0.079 0.096 Stroop 0.01 0.08 0.19 0.044 0.045 0.047 0.050 0.053 0.057 0.063 0.072 0.086 Garbled words 0.06 0.13 0.18 0.057 0.059 0.062 0.065 0.069 0.075 0.082 0.094 0.113 Price recall Beans (Week 1) -0.11 0.11 0.31 0.052 0.054 0.056 0.059 0.063 0.068 0.075 0.085 0.103 Corn (Week 1) -0.08 0.11 0.29 0.053 0.055 0.057 0.061 0.064 0.070 0.077 0.087 0.105 Goat (Week 1) 0.02 0.08 0.16 0.045 0.047 0.049 0.051 0.055 0.059 0.065 0.074 0.089 (B) Five waves Minimum Detectable Effect (absolute value) June coefficient June std. dev. Average T = 1250 T = 1125 T = 1000 T = 875 T = 750 T = 625 T = 500 T = 375 T = 250 Cognitive tasks Digit span 0.13 0.09 0.24 0.030 0.032 0.033 0.035 0.037 0.040 0.044 0.050 0.060 Stroop 0.01 0.08 0.19 0.028 0.029 0.030 0.031 0.033 0.036 0.040 0.045 0.055 Garbled words 0.06 0.13 0.18 0.036 0.037 0.039 0.041 0.044 0.047 0.052 0.059 0.072 Price recall Beans (Week 1) -0.11 0.11 0.31 0.033 0.034 0.036 0.037 0.040 0.043 0.047 0.054 0.065 Corn (Week 1) -0.08 0.11 0.29 0.034 0.035 0.036 0.038 0.041 0.044 0.048 0.055 0.067 Goat (Week 1) 0.02 0.08 0.16 0.028 0.030 0.031 0.032 0.035 0.037 0.041 0.047 0.057 Table 4 – Example for Digit Span (Week 2) under 1% significance Control group (Uninsured) Insured Insured Insured Insured Insured Insured Insured Insured Insured 5000 - Insured 1250 1125 1000 875 750 625 500 375 250 Waves 2 2 2 2 2 2 2 2 2 t_(1-κ) 2.58 2.58 2.58 2.58 2.58 2.58 2.58 2.58 2.58 t_α 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 p 0.25 0.225 0.2 0.175 0.15 0.125 0.1 0.075 0.05 σ 0.0926 0.0926 0.0926 0.0926 0.0926 0.0926 0.0926 0.0926 0.0926 MDE 0.048 0.050 0.052 0.055 0.058 0.063 0.069 0.079 0.096 Under 10% and 5% significance, both the two- and five-wave designs would be able to detect the effects for Digit span, Garbled words, and price recall of beans and corn. The five-wave design would be very close to detecting the effect of the treatment on recall of goat average prices. Under 1% significance, the two-wave design would no longer be able to detect the effect of the treatment on the score of Garbled words, while the five-wave design would still be able to detect it. None of the two designs would be able to detect the effect of the treatment on Stroop scores in week 1 or on recall of goat prices in week 2. Having said that, the estimated effects for the June wave were very small, so it might as well be that such effects are not statistically significant after the planting stage, when uncertainty about rainfall has been resolved. As an illustration, we estimated a four-fold effect of the treatment on stoop scores in the March wave. It follows that the number of waves is binding in this design in what comes to detecting the effects of interest, particularly with respect to Garbled words, the one task representing the “focus dividend” of tunneling in our 2014 pilot.