# **ANNEX. SURVEY-TO SURVEY IMPUTATION METHODOLOGY**

## **1. Methodology**

The estimates of poverty and welfare status of the households rely on survey data with a complex consumption module containing large set of detailed questions on prices and quantities consumed. Given its complexity the collection and analysis of that data involves significant investment of time, money and analytical efforts. On the other hand, there is a need for timely poverty estimates for evidence-based policies in the face of the high cost of fielding comprehensive surveys to track income and/or expenditure has led to the development of a variety of approaches for estimating poverty in the absence of consumption expenditure or income data.

In this section, we explore the survey-to-survey approach, which used the common observed assets and household characteristics in order to impute a proxy for welfare. The survey-to-survey imputation requires that at least one previous comparable survey contains household-level income or consumption information. The method draws upon the imputation literature (see Brick and Kalton, 1996 for a discussion of various techniques), which utilizes non-missing data in a larger data set to predict the values for missing variables, and from the poverty targeting literature (see Grosh and Baker, 1995) which seeks proxies for poverty status from household characteristics. The survey-to-survey imputation method extends that to using common variables in two data sets, only one of which contains consumption to predict consumption values in the second data set. A common application of this method in poverty analysis is “poverty mapping,” which uses consumption and poverty estimates from a household survey imputed into census data to achieve very fine levels of geographic disaggregation. (see Rao, 2003, for a discussion of the general technique of small area estimation, and Elbers et al., 2002, specifically related to poverty mapping.) For examples of surveyto-survey imputation for poverty analysis, see Stifel and Christiaensen (2007), Tarozzi (2007), Grosse et al (2009), and Douidich et al (2013).

A more formal presentation of the S2S model is as follows. There are surveys: in Survey 1 there are information on the income or consumption as well as the set of household characteristics ���. In the Survey 2, the same set of household characteristics are also observed, and those characteristics are comparable between the two surveys.

The (log) of per capita household income or consumption is modeled for the first survey as: ��� ��′������� where ��� is the per capita income or consumption of household _h_ residing in area _c_ , ��� are household and area/location characteristics, and ��� ��� ���� is the residual composed of the area component �� and the household component ���, which have zero expectations and are independent of each other.

In the second survey where there is no income or consumption information, a set of common variables ��� will be use to impute the income or consumption for each household in the second survey using the estimated points and their distributions estimated from the survey 1. Since each estimated point is fluctuated from an assumed normal distribution with its standard errors, the imputation is done through a number of simulation in order to preserve the error structure of the correlates.

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