The sampling errors can be reduced by increasing the size of the sample collected in the future round. The imputation errors can also be low since the models are estimated using a full sample. However, this approach requires the assumption that underlying parameter estimates in the imputation models remain stable over time. This could become controversial if a large structural change or economic shock occurs between a household survey with consumption data and a survey without consumption data. In the face of such shocks, the consumption models estimated from the household survey with consumption data might not reflect current consumption patterns accurately.

# **Data and “Full Sample Direct Estimation” Approach as a Benchmark**

Bangladesh has been conducting a nationally representative multitopic household survey every five years since 1995; poverty statistics are available every five years. Both the 2000 and 2005 HIESs have a very similar questionnaire and follow the same sampling design. Food consumption data were collected using daily diary forms for 200 items and weekly for 30 items. Nonfood consumption data were collected using monthly and yearly recall forms for about 50 and 150 nonfood items, respectively. Enumerators stayed in primary sampling units (PSUs) for around two weeks, and visited each household every two days to collect information on daily food consumption for two days. Also, enumerators visited the same households for two more days to collect data on nondaily food and nonfood consumption. The 2000 HIES has 14 strata and includes 7,440 households, while the 2005 HIES has 16 strata and includes 10,800 households. The number of PSUs ranges across strata. Each PSU had 10 or 20 households in 2000, and exactly 20 households in 2005. In total, the 2000 and 2005 HIESs had 442 and 504 PSUs, respectively.<sup>2</sup> Both the 2000 and 2005 HIESs selected PSUs following the probability-proportional-to-size (PPS) sampling while selecting households using the simple random sampling (SRS) from the selected PSUs.

The hybrid survey is constructed from the 2005 HIES data. Subsamples are drawn from the 2005 HIES data and include both consumption and nonconsumption data—procedures for selection of subsamples are explained in the next section. The full sample is the same as the 2005 HIES data, and except for households selected for the subsample, has only nonconsumption data. For the Full Imputation approach, consumption models are developed from the full sample of the 2000 HIES data. The models are applied to impute household expenditures into the entire 2005 HIES sample using nonconsumption data.

All three approaches produce poverty headcount rates at the national level and for urban and rural areas in 2005. A benchmark for all three approaches is the poverty statistics estimated from actual consumption data of the 2005 HIES data. This benchmark is the Full Sample Direct Estimation approach. As shown in table 1, the poverty headcount rate is 40.0 percent for the entire country, and 43.8 and 28.4 percent in rural and urban areas, respectively. The SEs are 1.1 percent for the entire country, and 1.3 and 1.9 percent, respectively, in the rural and urban areas.

**Table 1: Poverty Headcount Rates Using Full Sample of 2005 HIES**

|Full sample|Povert|yrates|95%|CI|Range of CI|
|---|---|---|---|---|---|
|National|40.0|(1.1)|37.8|42.2|4.5|
|Rural|43.8|(1.3)|41.3|46.3|4.9|
|Urban|28.4|(1.9)|24.6|32.1|7.5|

_Source_ : Authors’ estimations using 2005 HIES data. _Note_ : Parentheses are SEs. CI = confidence interval.

# **Subsample Selection in a Hybrid Survey**

To preserve the sampling design in the 2005 HIES, we followed its sampling as much as possible. For example, like the 2005 HIES, PSUs of a subsample were selected following PPS sampling (see Lohr 6