||the<br>shorter<br>questionnaire|to<br>shorter<br>questionnaire||inequality (Figure 1 and Figure<br>2) (Beegle et al. 2012)|
|---|---|---|---|---|
|**Cross-Survey**<br>**(X-Survey)**<br>**imputations**|Non-response is an<br>issue but not as<br>much<br>as<br>in<br>full<br>consumption due to<br>the<br>shorter<br>questionnaire|Very small issue as no<br>consumption section|Very small issue as<br>questions are simple|Reliance<br>on<br>old<br>data<br>introducing bias in structural<br>model<br>leading<br>to<br>biased<br>poverty estimates (Figure 3)|

Using the full consumption data from KIHBS 2015/16 as benchmark, in this section, first, we investigate the empirical trade-off between the number of core items and the number of optional modules for the rapid approach with respect to the performance of poverty indicators. Second, we compare the rapid approach with a traditional reduced consumption aggregate, without any adjustment of the poverty line. Third, we again use a reduced consumption aggregate, but adjust the poverty line based on previously observed consumption from 2005/6. Fourth, we compare the application of the rapid approach in the pilot in Kenya with a cross-survey imputation approach also using the 2005/6 data as baseline.

# **Trade-off with Number of Core Items and Optional Modules**

As discussed in the methodology section, the rapid approach creates a trade-off between the number of core items and the number of optional modules, as a larger number of core items (smaller number of optional modules) will improve the performance of the estimation. A larger number of core items will capture a larger fraction of the variance in the core module, minimizing the estimation error for the variance. Similarly, a smaller number of optional modules reduces the estimation error of the covariance between modules. However, the time savings by the rapid approach are larger for a smaller number of items in the core module and a larger number of optional modules as fewer items are asked about for each household.

**Table 2: Trade-off for FGT measures by number of optional modules and number of core items measured by bias and cv.**

||||Bia|s|||||CV||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|Opt.|||Core It|ems|||||Core It|ems|||
|Mod.|0|1|3|5|10|20|0|1|3|5|10|20|
|2|0.021|0.019|0.015|0.012|0.009|0.006|0.081|0.075|0.051|0.043|0.029|0.017|
|4<br>t0|0.033|0.032|0.024|0.019|0.014|0.007|0.125|0.122|0.085|0.07|0.051|0.026|
|6<br>fg|0.039|0.036|0.027|0.021|0.015|0.01|0.139|0.14|0.099|0.081|0.06|0.037|
|8|0.042|0.042|0.031|0.026|0.021|0.009|0.151|0.155|0.105|0.096|0.08|0.035|
|2|0.015|0.014|0.01|0.008|0.005|0.003|0.128|0.12|0.081|0.071|0.051|0.028|
|4<br>t1|0.024|0.023|0.016|0.013|0.009|0.005|0.19|0.189|0.129|0.114|0.087|0.045|
|6<br>fg|0.027|0.026|0.019|0.015|0.011|0.007|0.207|0.214|0.15|0.131|0.103|0.062|
|8|0.029|0.029|0.02|0.018|0.015|0.006|0.224|0.232|0.156|0.151|0.132|0.063|
|2|0.011|0.01|0.007|0.006|0.004|0.002|0.166|0.157|0.108|0.098|0.075|0.04|
|4<br>t2|0.017|0.017|0.012|0.01|0.007|0.004|0.241|0.241|0.166|0.154|0.123|0.064|
|6<br>fg|0.02|0.019|0.014|0.011|0.008|0.005|0.259|0.272|0.192|0.174|0.144|0.085|
|8|0.021|0.022|0.015|0.013|0.011|0.005|0.279|0.29|0.198|0.198|0.179|0.09|
|2|0.005|0.001|0.001|0|0.003|0.002|0.014|0.004|0.004|0.004|0.009|0.005|
|4<br>ini|0.004|0.001|0.003|0.001|0|0.003|0.013|0.009|0.01|0.004|0.004|0.01|
|6<br>g|0.009|0.005|0.005|0.008|0.006|0.008|0.025|0.014|0.014|0.021|0.015|0.021|
|8|0.001|0.008|0.011|0.003|0.006|0.007|0.011|0.022|0.03|0.01|0.015|0.018|

Based on simulations using KIHBS 2015/16, we estimate the bias and coefficient of variation to estimate FGT0, FGT1 and FGT2 as well as the Gini using as reference the full consumption aggregate from the 10