[1999, 108] for more details). For selection of households in select PSUs, we used the SRS and selected 10 households per PSU. We reduced the 20 households in the 2005 HIES to 10 to reduce the sampling error. To see the effects of sample size, this analysis used two different sizes for the subsample: 320 and 640. Note that increasing the size of the subsample increases the cost of data collection, but likely improves the precision of poverty estimates as well.

|**Table 2: Sampling Schemes and Biases in Poverty Estim**<br>|**ates**||
|---|---|---|
|Sampling scheme|Pover|tyrate|
|1. PPS to select 4 PSUs from each stratum and PPS to<br>select 10 households each|42.2|(2.4)|
|2. PPS to select 4 PSUs from each stratum and SRS to<br>select 10 households each|40.4|(3.7)|
|3. PPS to select PSUs of different size from each stratum<br>(64 PSUs in total)and SRS to select 10 households|40.2|(2.9)|
|_Source_: Authors’ estimations from 640 households from the 2005 HIES.<br>_Note_: SEs are inparentheses.|||

The process of selecting subsamples impacts the results. If we use actual consumption data from the 2005 HIES, the national poverty headcount rate is 40 percent (table 1). If we select the same number of PSUs (or four PSUs) from each of all 16 strata and select 10 households by PPS, then the poverty rate from the subsample is biased upward (table 2). If we keep the same number of PSUs from each stratum, but select households by SRS, then the national poverty rate is close to the true rate. Finally, if we use a different number of PSUs from each stratum based on population, then the national poverty estimate is very close to the true estimate and the SE also declines. This analysis used the third approach in table 2 to select a subsample from the 2005 HIES.

# **Imputation Process for Subsample**

The Subsample Imputation and Full Sample Imputation both involve imputation of household expenditures from an ancillary survey. The imputation process follows methodology developed in ELL (2003), which has two stages: first, a model of log per capita consumption expenditure of household _h_ (lnyh) is estimated in a subsample of the hybrid survey (in the case of Subsample Imputation) or the 2000 HIES data (in case of Full Sample Imputation). The model can be defined as where α is an intercept, Xch′ is the vector of explanatory variables for household _h_ and location _c_ , and β is the vector of regression coefficients, Z<sup>′</sup> is the vector of location specific variables, γ is the vector of coefficients, and uch is a residual. This residual is decomposed into two independent components: uch = ηc + εch with a cluster-specific effect, ηc, and a household-specific effect, εch . This structure allows both a location effect—common to all households in the same area—and heteroskedasticity in the household-specific errors. The location variables can be at any level— _zila, upazila_ , union, _mauza_ , and village (in the case of Bangladesh)—and can be drawn from any data sources that include all locations in the country. All parameters regarding the regression coefficients ( α, β, γ ) and distributions of the disturbance terms are estimated by feasible generalized least squares. In the second stage, poverty estimates and their SEs are computed. There are two sources of errors involved in the estimation process: errors in the estimated regression coefficients (α�, β̂, γ�) and in the estimated residuals, both of which affect poverty estimates and the level of their accuracy. ELL (2003) propose a way to properly calculate poverty estimates as well as their SEs while taking into account these sources of bias. A simulated value of expenditure for each census household is calculated with predicted log expenditure α�+ Xh′ β̂ + Z′γ� and 7