Integrating Social Protection Strategies for Improved Impact: A Comparative Evaluation of Cash Transfers and Index Insurance in Kenya

Abstract

Social protection programmes aim to use public funds to reduce poverty and vulnerability. Cash transfers have proven to be an effective social protection strategy in many contexts but are extremely expensive. Researchers have suggested that integrating multiple interventions could improve the efficiency of protection programmes, but there are few evidence-based recommendations on how to best implement such approaches. This study uses household-level panel data to estimate the marginal impacts of observed cash and index insurance transfers (subsidies) on household income in northern Kenya. Those estimates are used to simulate sample-level poverty indices as the outcome of a standard cash transfer programme and of a similar programme that reallocates a small portion of the budget as an insurance subsidy to the vulnerable. We find that the integrated programme reduces poverty to a greater degree than do cash transfers alone, highlighting the importance of protecting the vulnerable in addition to supporting the poorest.

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Note: The left-most bars correspond to the top items in each legend

Notes

  1. 1.

    Conway et al. (2000).

  2. 2.

    For reviews of the literature, see Arnold et al. (2011); Fiszbein and Schady (2009).

  3. 3.

    de Janvry and Sadoulet (2006); Ross (1991).

  4. 4.

    For example, Barnett et al. (2008); Barrett et al. (2007).

  5. 5.

    Cai et al. (2015); Cole et al. (2013); Hill et al. (2017); Janzen and Carter (2013); Jensen et al. (2017a); Karlan et al. (2014); Mobarak and Rosenzweig (2013).

  6. 6.

    Binswanger-Mkhize (2012); Miranda and Farrin (2012); Mobarak and Rosenzweig (2013); Tobacman et al. (2017).

  7. 7.

    Alderman and Haque (2007); Carter and Janzen (2015); Devereux (2001); Janzen et al. (2016); Oxford Policy Management (2016).

  8. 8.

    Carter and Janzen (2015); Ikegami et al. (2016).

  9. 9.

    Foster et al. (1984).

  10. 10.

    McPeak et al. (2009).

  11. 11.

    Catley et al. (2013); McPeak et al. (2011).

  12. 12.

    OCHA (2011a, b).

  13. 13.

    Hurrell and Sabates-Wheeler (2013); Jensen et al. (2014).

  14. 14.

    Sublocation is an administrative unit following county, division and location.

  15. 15.

    NDMA (2016).

  16. 16.

    Fitzgibbon (2014).

  17. 17.

    See the National Drought Management Agency (2016) for more details on targeting and procedures for the emergency contingent transfers.

  18. 18.

    Chantarat et al. (2013).

  19. 19.

    The base premium rates were constant for the period examined by this research.

  20. 20.

    Janzen and Carter (2013); Jensen et al. (2017a).

  21. 21.

    In addition, Tafere et al. (2015) found that IBLI increased subjective well-being in the nearby Borena Zone of Southern Ethiopia.

  22. 22.

    A tropical livestock unit (TLU) is a common unit for standardising livestock based on average metabolic weights and is as follows: TLU = 1 cow = 0.7 camels = 10 goats or sheep.

  23. 23.

    Little et al. (2008); Toth (2015).

  24. 24.

    Chantarat et al. (2014); Ikegami et al. (2015); Jensen et al. (2017a).

  25. 25.

    Although guaranteed HSNP transfers could be used to relieve a liquidity constraint and/or a risk constraint, it is not clear a priori whether households will use transfers to buy more animals to increase production or will sell off animals being held as precautionary savings. Although IBLI does not relieve a liquidity constraint, if herd sizes without insurance are risk constrained, they should increase with insurance coverage, but if they reflect precautionary savings, they should fall with insurance coverage.

  26. 26.

    We would have preferred to include current and all potential lags in participation in order to include complete information on historic programme participation. However, there is a trade-off between increased lags in programme participation and standard errors, as well as a loss of power (increased bias) in our IV regression as the number of instrumented variables becomes large. We compromise by incorporating a single lag in order to maintain some amount of statistical power while continuing to focus on effects lasting beyond an immediate season.

  27. 27.

    NDMA (2016).

  28. 28.

    Recall that HSNP is present in only the four poorest counties in Kenya, so that the threshold used to identify the poorest 27 per cent of households does not generalise to all of Kenya. This study employed household data from one of those four counties, Marsabit County.

  29. 29.

    Jensen et al. (2017a, b).

  30. 30.

    Specifically, the index is equal to one when the cumulative of the aggregated standardised NDVI values in a region are below the 25th per centile of within index division observed seasonal values. The 25th percentile was appropriate because the region experienced two large droughts during the 10-season survey period.

  31. 31.

    Although the first IBLI survey was collected in October and November of 2009, just after HSNP I started making bi-monthly transfers, many of its questions collect data on monthly and seasonal household attributes, providing information on pre-HSNP characteristics.

  32. 32.

    Ikegami and Sheahan (2015).

  33. 33.

    Exogenous variation in prices, and thus demand, offers an empirical approach for causal inference with respect to the impact of purchasing IBLI.

  34. 34.

    A description of variable construction and the full summary statistics are provided in Appendix A.

  35. 35.

    This figure was set to be 75 per cent of the value of a food aid ratio as set by the World Food Programme in 2006 (Hurrell and Sabates-Wheeler 2013).

  36. 36.

    HSNP’s objectives can be found on their website at http://www.hsnp.or.ke/index.php/as/objectives.

  37. 37.

    Earth Observatory (2009).

  38. 38.

    For example, Takahashi et al. (2016).

  39. 39.

    The baseline premiums offered to households were 40 per cent less than the commercial rate. That flat subsidy came before the additional subsidy offered by the coupon discounts.

  40. 40.

    The expected purchase is the product of the predicted likelihood of purchasing from a probit model and the predicted level of demand. The resulting distribution of expected purchases contains many small (<0.1 TLU = 1 goat or sheep) values. For the summary statistics in the text, we focus on those greater than 0.1, but all levels of expected purchases had the opportunity to impact outcomes.

  41. 41.

    Note that the 72 per cent reduction in demand due to a 66 per cent increase in price implies a price elasticity of demand equal to −1.09.

  42. 42.

    Note that programme participation is lagged by one period, so that there are no programme impacts in the first period (SRSD2008).

  43. 43.

    We should note that although HSNP II-type extensive scaling is no different from an insurance transfer logistically, there are plenty of reasons (e.g. differences in framing, transfer agents, contracts) that the outcomes of such a cash transfer could be very different from that of an identical insurance transfer.

  44. 44.

    See Jensen et al. (2014) for a discussion of sampling differences and their implications for the data between the HSNP I and the IBLI survey.

  45. 45.

    Hurrell and Sabates-Wheeler (2013).

  46. 46.

    Analysis available upon request.

References

  1. Alderman, H. and Haque, T. (2007) ‘Insurance against covariate shocks: The role of index-based insurance in social protection in low-income countries of Africa’, World Bank Working Paper 95, Washington, DC: World Bank, Africa Region Human Development Department.

  2. Arnold, C., Conway, T. and Greenslade, M. (2011) Cash Transfers Literature Review, London: Department for International Development.

    Google Scholar 

  3. Barnett, B.J., Barrett, C.B. and Skees, J.R. (2008) ‘Poverty traps and index-based risk transfer products’, World Development 36(10): 1766–1785.

    Article  Google Scholar 

  4. Barrett, C.B., Barnett, B.J., Carter, M.R., Chantarat, S., Hansen, J.W., Mude, A.G., Osgood, D.E., Skees, J.R., Turvey, C.G. and Neil Ward, M. (2007) ‘Poverty traps and climate risk: limitations and opportunities of index-based risk financing’, IRI Technical Report 07-02.

  5. Binswanger-Mkhize, H.P. (2012) ‘Is there too much hype about index-based agricultural insurance?’, Journal of Development studies 48(2): 187–200.

    Article  Google Scholar 

  6. Cai, H., Chen, Y., Fang, H. and Zhou, L. (2015) ‘The effect of microinsurance on economic activities: Evidence from a randomized natural field experiment’, The Review of Economics and Statistics 97(2): 287–300.

    Article  Google Scholar 

  7. Carter, M.R. and Janzen, S.A. (2015) ‘Social protection in the face of climate change: Targeting principles and financing mechanisms’, World Bank Policy Research Working Paper 7476.

  8. Catley, A., Lind, J. and Scoones, I. (2013) Pastoralism and Development in Africa: Dynamic Change at the Margins, London: Routledge.

  9. Chantarat, S., Mude, A.G., Barrett, C.B. and Carter, M.R. (2013) ‘Designing index-based livestock insurance for managing asset risk in Northern Kenya’, The Journal of Risk and Insurance 80(1): 205–237.

    Article  Google Scholar 

  10. Chantarat, S. et al. (2014) Welfare impacts of index insurance in the presence of a poverty trap. World Development 94: 119–138.

    Article  Google Scholar 

  11. Cole, S., Giné, X. and Vickery, J. (2013) ‘How does risk management influence production decisions? Evidence from a field experiment’, World Bank Policy Research Working Paper #6546.

  12. Conway, T., de Hann, A. and Norton, A. (eds) (2000) Social Protection: New Directions of Donor Agencies, London: Department for International Development.

  13. de Janvry, A. and Sadoulet, E. (2006) ‘Making conditional cash transfer programs more efficient: designing for maximum effect of the conditionality’, The World Bank Economic Review 20(1): 1–29.

    Article  Google Scholar 

  14. Devereux, S. (2001) ‘Livelihood insecurity and social protection: A re‐emerging issue in rural development’, Development Policy Review 19(4): 507–519.

    Article  Google Scholar 

  15. Earth Observatory (2009) http://earthobservatory.nasa.gov/NaturalHazards/view.php?id=39363, Retrieved 10 February 2016.

  16. Fiszbein, A. and Schady, N. (2009) Conditional Cash Transfers: Reducing Present and Future Poverty, World Bank Publications.

  17. Fitzgibbon, C. (2014) HSNP Phase II Registration and Targeting Lessons Learned and Recommendations, London: Department of International Development (DFID).

  18. Foster, J., Greer, J. and Thorbecke, E. (1984) ‘A class of decomposable poverty measures’, Econometrica 52: 761–766.

    Article  Google Scholar 

  19. Hill, R.V., Kumar, N., Magnan, N., Makhija, S., de Nicola, F., Spielman, D.J. and Ward, P.S. (2017) ‘Insuring against droughts: Evidence on agricultural intensification and index insurance demand from a randomized evaluation in rural Bangladesh’, IFPRI Discussion Paper No. 1630, 40.

  20. Hurrell, A. and Sabates-Wheeler, R. (2013) ‘Kenya hunger safety net programme monitoring and quantitative’, Impact Evaluation Final Report: 2009 to 2012.

  21. Ikegami, M., Barrett, C.B. and Chantarat, S. (2015) ‘Dynamic effects of index based livestock insurance on household intertemporal behavior and welfare’. Unpublished.

  22. Ikegami, M., Carter, M.R., Barrett, C.B. and Janzen, S.A. (2016) ‘Poverty traps and the social protection paradox’, NBER Working Paper No. 22714.

  23. Ikegami, M. and Sheahan, M. (2015) Index Based Livestock Insurance (IBLI) Marsabit Household Survey Codebook, ILRI.

  24. Janzen, S.A. and Carter, M.R. (2013) ‘After the drought: The impact of microinsurance on consumption smoothing and asset protection’, NBER Working Paper No. 19702.

  25. Janzen, S.A., Jensen, N.D. and Mude, A.G. (2016) ‘Targeted social protection in a pastoralist economy: Case study from Kenya’, Revue Scientifique et Technique-Office International des Epizooties 35(2): 587–596.

    Article  Google Scholar 

  26. Jensen, N.D., Barrett, C.B. and Mude, A. (2017a) ‘Index insurance and cash transfers: A comparative analysis from northern Kenya’. Unpublished.

  27. Jensen, N.D., Mude, A. and Barrett, C.B. (2017b) ‘How basis risk and spatiotemporal adverse selection influence demand for index insurance: Evidence from northern Kenya’. Unpublished.

  28. Jensen, N., Sheahan, M., Barrett, C.B. and Mude, A. (2014) ‘Hunger Safety Net Program (HSNP) and Index Based Livestock Insurance (IBLI) baseline comparison’.

  29. Karlan, D., Osei, R., Osei-Akoto, I. and Udry, C. (2014) ‘Agricultural decisions after relaxing credit and risk constraints’, The Quarterly Journal of Economics 129(2): 597–652.

    Article  Google Scholar 

  30. Little, P.D., McPeak, J., Barrett, C.B. and Kristjanson, P. (2008) ‘Challenging orthodoxies: Understanding poverty in pastoral areas of East Africa’, Development and Change 39(4): 587–611.

    Article  Google Scholar 

  31. McPeak, J., Doss, C., Barrett, B. and Kristjanson, P. (2009) ‘Do community members share development priorities? Results of a ranking exercise in east African rangelands’, Journal of Development Studies 45(10): 1663–1683.

    Article  Google Scholar 

  32. McPeak, J.G., Little, P.D. and Doss, C.R. (2011) Risk and Social Change in an Africa Rural Economy: Livelihoods in Pastoralist Communities (Vol. 7), London: Routeledge.

  33. Miranda, M.J. and Farrin, K. (2012) ‘Index insurance for developing countries’, Applied Economic Perspectives and Policy 34(3): 391–427.

    Article  Google Scholar 

  34. Mobarak, A.M. and Rosenzweig, M.R. (2013) ‘Informal risk sharing, index insurance, and risk taking in developing countries’, The American Economic Review 103(3): 375–380.

    Article  Google Scholar 

  35. National Drought Management Agency (NDMA) (2016) ‘Hunger safety net programme scalability guidelines guidance for scaling up HSNP payments’.

  36. OCHA (2011a) Eastern Africa: Drought – Humanitarian Snapshot as of 24 June 2011. http://www.fews.net/sites/default/files/documents/reports/Horn_of_Africa_Drought_2011_06.pdf.

  37. OCHA (2011b) Eastern Africa: Drought – Humanitarian Snapshot as of 20 Jul 2011. http://www.fews.net/sites/default/files/documents/reports/Horn_of_Africa_Crisis_2011_07.pdf.

  38. Oxford Policy Management (2016) DFID Shock-Responsive Social Protection Systems Research: Literature Review, Oxford, UK: Oxford Policy Management.

    Google Scholar 

  39. Ross, T.W. (1991) ‘On the relative efficiency of cash transfers and subsidies’, Economic Inquiry 29(3): 485–496.

    Article  Google Scholar 

  40. Tafere, K., Barrett, C.B., Lentz, E. and Birhanu T.A. (2015) ‘The subjective well-being gains from insurance that doesn’t pay out’. Unpublished.

  41. Takahashi, K., Ikegami, M., Sheahan, M. and Barrett, C.B. (2016) Experimental evidence on the drivers of index-based livestock insurance demand in southern Ethiopia, World Development 78: 324–340.

    Article  Google Scholar 

  42. Tobacman, J., Stein, D., Shah, V., Litvine, L., Cole, S. and Chattopadhyay, R. (2017) ‘Formal insurance against weather shocks evidence from a randomized control trial in India’. Unpublished.

  43. Toth, R. (2015) ‘Traps and thresholds in pastoralist mobility’, American Journal of Agricultural Economics 97(1): 315–332.

    Article  Google Scholar 

Download references

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Correspondence to Nathaniel Jensen.

Appendices

Appendix A: Description of key variables and summary statistics

See Table A1.

Table A1 Definition of variables and descriptive statistics in the first season (SRSD 2008)

Appendix B: HSNP and IBLI instrumental variables

This section provides details of the HSNP and IBLI instrumental processes.

HSNP

Programme participation in HSNP I is neither random nor is there perfect targeting.29 As a precaution against endogenous participation, we instrumented for HSNP I participation. In theory, we had three exogenous sources of variation in participation at our disposal. The first was within-individual and captures the periods before and after HSNP receipt as well as changes to the transfer amount. The baseline IBLI survey collected data from before the first HSNP I transfers were made and, for HSNP, target sublocations were randomly designated into early and late categories. In addition, the HSNP rollout was staggered across sublocations in each early and late category.

The second source of exogeneity was between communities—HSNP I randomly targeted communities from a list of communities. Unfortunately, the list excluded a subset of communities deemed too insecure for the programme officers. While we were unable to observe if the surveyed non-HSNP I communities were or were not included in the list used for randomisation, households from the seven IBLI survey communities that were not targeted by HSNP I did have statistically significant differences at baseline from the HSNP I communities, indicating that some of them may not have been on that list or that small sample statistics were an issue here (Table B1).Footnote 44

Table B1 Summary statistics of HSNP and non-HSNP sublocations in SRSD2008

Thus, the between-community variation in participation was, in part, correlated to the variables of interest and could have posed more of a problem than a tool. We argue that such differences are largely due to community-level fixed effects, such as access to markets, remoteness, security and infrastructure. In that case, a household fixed effects model would address those issues. As a precaution against remaining differences, we included interactions between period and index division, which capture differences in average changes across seasons between index divisions. In Table B2, the robustness of our estimates to these assumptions was checked by examining the estimated mean impacts of HSNP on participants, while varying the sublocations included in the analysis. No statistically significant differences were found (Table B2, last row).

Table B2 Testing for robustness of estimated impact of HSNP across subsamples and the entire sample

HSNP I’s targeting criteria offered a third source of exogenous variation in participation. As appropriate targeting was a critical determinant of HSNP’s overall impact, the first phase randomised the beneficiary selection criteria at the sublocation level across three targeting mechanisms: age-based, dependency ratio and community-based targeting (CBT). If compliance had been perfect, we could have controlled for the targeting dimension (assuming that we observed it) and eligibility would have been exogenous. Unfortunately, HSNP targeting compliance was far from perfect.29 However, assuming partial compliance, the intended eligibility criteria would still generate exogenous variation in participation and thus could also be used as an instrument variable.

The community-based targeting (CBT) presents a difficulty with respect to the above strategy. We did not observe the CBT process nor did we have information on the dimensions used by community members for their targeting. HSNP’s own impact evaluation provided some insight into the process though. In it, Hurrell and Sabates-WheelerFootnote 45 controlled for household characteristics that were likely to have played a role in the CBT. We used a similar set of those characteristics from the period before the first transfers in each CBT sublocation and employed a probit model to predict the likelihood of HSNP participation in each CBT sublocation. We then constructed a household-level intent-to-treat variable within each CBT sublocation that was equal to one if the predicted likelihood of HSNP participation was greater than 50 per cent. By this approach, the generated intent-to-treat variable correctly sorted 69 per cent of households in each CBT sublocation during the season that HSNP launched in that sublocation.Footnote 46

Altogether, we had three potential sources of exogenous variation, one that distinguished between targeted and non-targeted sublocations, one that captured variation in date of initial transfers and variation in transfer size and one that helped distinguish which households within a target community were most likely to have received a transfer.

The first stage used to instrument for HSNP participation is described by Equation B.1.

$${\text{HSNP}}_{lit} = \delta_{0} + \delta_{1} {\text{ITT}}_{lit} + \delta_{2} X_{li1} + \delta_{lt} + \varepsilon_{lit},$$
(B.1)

where

$${\text{ITT}}_{it} = \left[ {\begin{array}{*{20}l} 1 \hfill & {{\text{if }}A_{li} = 1 {\text{and }}L_{lt}^{A} = 1 {\text{and }}S_{lt} = 1 } \hfill \\ 1 \hfill & {{\text{if }}B_{li} = 1 {\text{and }}L_{lt}^{B} = 1 {\text{and }}S_{lt} = 1} \hfill \\ 1 \hfill & {{\text{if }}C_{li} = 1 {\text{and }}L_{lt}^{C} = 1 {\text{and}}\;S_{lt} = 1} \hfill \\ 0 \hfill & {\text{otherwise}} \hfill \\ \end{array} } \right]$$
$$A_{li} = \left[ {\begin{array}{*{20}c} 0 & {\hbox{max}\; {\text{household age}}_{li1} < 64} \\ 1 & {\hbox{max}\; {\text{household age}}_{li1} \ge 64} \\ \end{array} } \right]$$
$$B_{li} = \left[ {\begin{array}{*{20}c} 0 & {{\text{dependency ratio}}_{li1} < 0.54} \\ 1 & {{\text{dependency ratio}}_{li1} \ge 0.54} \\ \end{array} } \right]$$
$$\begin{aligned} C_{li} = \left[ {\begin{array}{*{20}c} 0 & {\hat{p}_{{lit}} , < \,0.5} \\ 1 & {\hat{p}_{{lit}} , \ge \,0.5} \\ \end{array} } \right] , \quad p_{{lit^{\prime } }} = \gamma_{0} + \gamma_{0} X_{{lit^{\prime } }} + \varepsilon_{li1}, \hfill \\ {\text{where }}p_{{lit^{\prime } }} = 1\quad {\text{if }}S_{{l,t^{\prime } }} = 0, S_{{l,t^{\prime } + 1}} = 1\quad {\text{and}}\quad L_{l}^{C} = 1; \hfill \\ \end{aligned}$$
$$L_{l}^{A} = 1\quad {\text{if sublocation }}l \,{\text{is an age-targeted community}};$$
$$L_{l}^{B} = 1 \quad{\text{if sublocation }}l \,{\text{is a dependency ratio-targeted community }};$$
$$L_{l}^{C} = 1 \quad{\text{if sublocation }}l \,{\text{is a CBT-targeted community }};$$
$$S_{lt} = 1 \quad {\text{if HSNP transfers are being distributed in sublocation }}l {\text{in time period }}t;$$
$$X_{li1} = {\text{Baseline household characteristics including maximum age}}, {\text{dependency ratio, and }}\hat{p}_{li1};$$
$$\delta_{{{\text{l}}t}} = {\text{Index division * period fixed effects}}.$$

As mentioned above, this approach has a few potential issues. First, there were statistically significant differences in the observed means of household characteristics in HSNP and non-HSNP sublocations, a possible symptom of fundamental differences that could conflate our estimates. If those differences extended beyond levels to rates of change, this would mean that the non-HSNP communities were not a valid counterfactual and should not have been included in this analysis. The second was that we did not observe the CBT ranking, and our generated ranking may perform poorly as an ITT variable.

To determine the magnitude of these potential issues, we ran our main regression, excluding the IBLI variables, in three ways: (1) using only dependency ratio- and age-targeted HSNP sublocations, (2) using all non-HSNP sublocations and dependency ratio- and age-targeted HSNP sublocations and (3) using the entire sample including CBT sublocations (Table B2). Although there are a few small changes to the parameter estimates between the three models, all were the same sign, none were statistically different and all were within an order of magnitude. We also estimated the average impact among participants. The results are found at the bottom of Table B2. All three estimates are indistinguishable from zero and statistically indistinguishable from each other. We erred on the side of power and used the full sample in the main analysis.

Using the full sample, we regressed HSNP participation onto the ITT variable to provide some indication of the strength of our IV (Table B3). Here we saw that the IV alone was able to account for about 40 per cent of the variation that we observed in participation and the correlation was robust to index region-period controls and household fixed effects.

Table B3 The impact of HNSP’s intent-to-treat on likelihood of HSNP participation (OLS)

IBLI

There was also a risk of endogeneity in IBLI purchases. To identify the causal impacts of IBLI purchases, we used exogenous variation in IBLI purchasing behaviour, which was caused by the random distribution of premium discounts.

Before each sales season, premium discount coupons were randomly distributed to 60 per cent of the sample. The discounts provided by the coupons ranged from 10 to 60 per cent and were only valid for the sales season immediately following their distribution. By LRLD2013, 2,472 coupons had been distributed to the households. Because there had been six distribution events, nearly every household had received at least one discount coupon, and most households had received more than one coupon (Table B4).

Table B4 Number of discount coupons received by each household by LRLD2013

The log-level of discount had a strong and positive impact on the log-level of coverage purchased (Table B5). The discount elasticity of demand was near 0.4.

Table B5 Impact of discounts provided by coupons on IBLI purchases

Appendix C: Demand for insurance

We assume that households make their demand decisions in two steps. First, they choose whether to purchase. Second, they choose how much to purchase provided they have chosen to purchase. The assumption that these are two different decisions allows factors to affect one aspect of demand without affecting the other. For example, in our study, a household’s trust in the vender or the distance from a household to the nearest vender may have been an extremely important factor in one decision but not in the other. The parameter estimates are found in Table C1. We include the full set of covariates included in the main regression. The implied average marginal price elasticities of demand are included at the bottom of the table. Note that the final sales season (LRLD2013) was not used in these demand equations because that season was not used in the main analysis due to lagging.

Table C1 IBLI demand equation estimates

Appendix D: Bootstrapping

We used a bootstrapping process to inform on the precision of the FGT estimates and to test for differences between the programmes. To do so, we used a double bootstrapping approach to transform bootstrapped estimates into t-statistics, which were then used to identify the 95 per cent confidence intervals around the original estimates.

A summary of that process follows. Here we used the subscripts FULL, BOOT and REBOOT to indicate that a statistic was estimated using the full original sample (FULL), a sample developed by resampling with replacement from the full original sample (BOOT) and a sample developed by resampling with replacement from the BOOT sample (REBOOT), respectively.

  1. 1.

    Estimate the FGT metrics using the full sample generating the estimates described in Eqs. (1) and (2) in this article: \(\widehat{\text{FGT}}_{\text{FULL}}^{\alpha }\).

  2. 2.

    Resample with replacement from the full sample to generate the sample BOOT.

  3. 3.

    Use the resample to estimate the FGT metrics: \(\widehat{\text{FGT}}_{\text{BOOT}}^{\alpha }\).

  4. 4.

    Resample with replacement from BOOT, generating the sample REBOOT.

  5. 5.

    Estimate the FGT metrics using the REBOOT sample: \(\widehat{\text{FGT}}_{\text{BOOT, REBOOT}}^{\alpha }\)

  6. 6.

    Repeat steps 4–5, A times.

  7. 7.

    Repeat steps 2–6, B times.

Steps (1)–(7) result in three sets of estimates. For ease, we use the characters \(\tau , \varphi , {\text{and}} \omega\) to reference each set.

$$\tau = \left\{ {\widehat{\text{FGT}}_{\text{FULL}}^{\alpha } } \right\}; \varphi = \left\{ {\widehat{\text{FGT}}_{1}^{\alpha } , \ldots , \widehat{\text{FGT}}_{A}^{\alpha } } \right\} ; \omega = \left\{ {\widehat{\text{FGT}}_{1,1}^{\alpha } , \ldots , \widehat{\text{FGT}}_{1,B}^{\alpha } , \widehat{\text{FGT}}_{2,1}^{\alpha } , \ldots , \ldots , \widehat{\text{FGT}}_{A,B}^{\alpha } } \right\}.$$

The above estimates are used to develop confidence intervals around \(\widehat{\text{FGT}}_{\text{FULL}}^{\alpha }\) as follows:

$${\text{CI}}^{\rho } = \left[ {\widehat{\text{FGT}}_{\text{FULL}}^{\alpha } - t^{{{\raise0.7ex\hbox{$\rho $} \!\mathord{\left/ {\vphantom {\rho 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} *SE_{{\widehat{\text{FGT}}_{\text{FULL}}^{\alpha } }} ; \widehat{\text{FGT}}_{\text{FULL}}^{\alpha } + t^{{(1 - {\raise0.7ex\hbox{$\rho $} \!\mathord{\left/ {\vphantom {\rho 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}})}} *{\text{SE}}_{{\widehat{\text{FGT}}_{\text{FULL}}^{\alpha } }} } \right],$$

where

$${\text{SE}}_{{\widehat{\text{FGT}}_{\text{FULL}}^{\alpha } }} = \frac{{\sigma_{\varphi } }}{\sqrt A }$$
$$t^{{{\raise0.7ex\hbox{$\rho $} \!\mathord{\left/ {\vphantom {\rho 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}}} = {\text{the}}\,{\raise0.7ex\hbox{$\rho $} \!\mathord{\left/ {\vphantom {\rho 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}{\text{th ranked}}\, t_{i} ;\, t_{i} = \frac{{\widehat{\text{FGT}}_{\text{FULL}}^{\alpha } - \widehat{\text{FGT}}_{\text{BOOT}}^{\alpha } }}{{{\text{SE}}_{{\widehat{\text{FGT}}_{\text{BOOT}}^{\alpha } }} }}$$
$${\text{SE}}_{{\widehat{\text{FGT}}_{i}^{\alpha } }} = \frac{{\sigma_{i,\omega } }}{\sqrt B }.$$

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Jensen, N., Ikegami, M. & Mude, A. Integrating Social Protection Strategies for Improved Impact: A Comparative Evaluation of Cash Transfers and Index Insurance in Kenya. Geneva Pap Risk Insur Issues Pract 42, 675–707 (2017). https://doi.org/10.1057/s41288-017-0060-5

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Keywords

  • social protection
  • HSNP
  • index-based livestock insurance
  • pastoralists
  • social welfare