a few core items with highest consumption shares, even if they are selected from a rather outdated survey as in Kenya with a 10-year gap.

The approach of using an adjusted poverty line performs significantly better than the simple reduced approach presented in the previous section, but at the cost of the distributional shape captured in the Gini coefficient. For the FGT measures, it is, thus, generally advisable to adjust the poverty line if a reduced approach must be used, even if the adjustment is based on outdated consumption shares from an old survey. For FGT0, the average bias of the adjusted reduced approach is usually around or above the maximum bias of the rapid approach. Furthermore, the maximum bias is considerably larger than the average bias for the adjusted, reduced approach compared to the rapid approach. For FGT1, the average bias of the adjusted, reduced approach becomes more comparable with the rapid approach, but the maximum bias is still significantly larger than the maximum bias of the rapid approach. For FGT2, the performance of the adjusted, reduced approach becomes more difficult to interpret. The Gini coefficient is not well conserved approaching a bias of 0.05 for highest time savings.

As the results show, the adjusted, reduced approach has larger variation across poverty lines (as shown by the larger difference between average and maximum bias) as well as across the different number of items (implying different time savings). The definition of the estimator explains this. The estimator depends strongly on the items selected for the reduced approach, as the accuracy relies on the adjustment factor of the poverty line, which is the share captured by those items. The error can be decomposed into two components. The first component is the change of the distributional shape between the survey used for the adjustment and the application of the adjusted poverty line. The second component depends on the difference in the share captured by those items between the two surveys. Both errors become zero if the approach is implemented for the same population at the same time. In the usual case though, neither the population nor the time point is the same. In these cases, especially the second component of the error leads to large variation of the performance. Even though the consumption shares of the items can change, the changes might cancel out leading to a good performance of the approach. However, adding one more item to the consumption module can void the cancellation, leading to a worse performance. Without knowing the share of the items from total consumption (which is not measured), it is impossible to predict how many items should be selected for a good performance of the approach.

# **Application to Kenya: Rapid vs. Cross-Survey Estimation**

In 2015/16, a CAPI pilot was implemented alongside KIHBS 2015/16 using the rapid approach. While the configuration is conservative with only 30 percent time savings, the results show impressive performance for all FGT measures (Figure 3) in comparison with the full consumption as estimated for KIHBS 2015/16. Across all potential poverty lines, the rapid approach has a bias of below 1.3 percentage points for FGT0, 0.7 percentage point for FGT1 and 0.6 percentage point for FGT2. The Gini has a bias of only 0.012.

We compare the performance with a cross-survey imputation of consumption using a structural model built based on the KIHBS 2005/6 data set and applied to KIHBS 2015/16, ignoring the collected consumption data in 2015/16. The performance of the structural model is then assessed against the KIHBS 14