rounds in which consumption data were collected by diary. Therefore, even if the recall approach is cost saving, it is not recommended for the calculation of poverty estimates.

# **VI. Conclusion**

Despite suggestive empirical evidence provided by Christiaensen et al. (2012), imputing household expenditure or income using models estimated from past data is risky because there is no guarantee that consumption models will not change over time. For example, even Christiaensen et al. (2012) show the consumption models estimated from past data could not predict future poverty data in the Russian Federation. They argued that the divergence in poverty rates between direct estimation and imputation can be attributed to questionable inflation adjustments, but it is difficult to prove that the inflation adjustment is the only source of the divergence.

The biggest challenge for the existing imputation approach is that if consumption or income data are not collected, there is no way to test whether the imputed poverty rate is correct until new consumption data are collected in the future. Christiaensen et al. (2012) could test the accuracy of their imputation model because they could compare the imputed consumption data with the actual consumption data. But, if we truly move to the imputation approach, except for big survey years, only nonconsumption data will be collected and poverty rates will be estimated using imputed consumption data. The accuracy of the poverty rates calculated using imputed consumption data cannot be tested in years when only nonconsumption data are available.

This paper provides empirical evidence that a hybrid approach—collecting consumption data for a subsample only—can be extremely useful in improving the statistical reliability of poverty data. For example, collecting consumption data from a subsample enables us to produce consistent but likely noisy poverty estimates by directly estimating them from the subsample. These estimates can be used to examine whether imputed poverty rates are accurate. Furthermore, this analysis shows that if consumption models are developed from the subsample, poverty rates can be estimated reliably by applying the consumption models to a large sample of the nonconsumption data. The estimates based on the Subsample Imputation approach are shown to be as precise as, or even better than, those based on models estimated from past data, even if the size of a subsample is as small as 320, at least as far as poverty estimates at the national level are concerned. Another advantage of the Subsample Imputation approach is that consumption models reflect the contemporaneous relationship between consumption data and nonconsumption data, which is not the case for the approach proposed and tested by Christiaensen et al. (2012).

Subsample Imputation, or even Subsample Direct Estimation, is very attractive, but there is one challenge to overcome, particularly in the case of Bangladesh, where poverty lines are updated with inflation rates estimated for each of the 16 strata separately. The official method constructs food inflation rates based on unit values calculated from HIES consumption data. If consumption data are collected only from a subsample, the number of unit values will be very limited, and thus, the reliability of unit values will be questionable. This is particularly true because unit values are known to be much noisier than price data.

However, evidence from the pilot survey suggests that unit values for key consumption items are not so noisy and quite similar to price data. Also, this analysis shows that even if unit values from a subsample are used to estimate inflation rates and poverty lines, the estimates are quite accurate. As a result, poverty rates estimated via either the Subsample Imputation or Subsample Direct Estimation are quite precise, even when the consumption models as well as the price adjustments are made using consumption data from a small subsample.

When determining which approach to use, implementation cost is also an important consideration. Subsample Imputation needs a large sample with nonconsumption data, and a small subsample with both consumption and nonconsumption data. If the subsample size is 640, then this combined survey needs 25