# **3.2. Empirical approach**

The main question we attempt to address is whether, and how, the CPI price data is useful for spatial price adjustment in poverty measurement, given the importance of detailed product quality information. To empirically examine it in this case study of Ghana, we compare the results of various spatial price measurement methods. The main methods we test are (a) the bilateral/multilateral price index approach, (b) the CPD approach, and (c) the Engel curve approach. The main data sets include (a) the market price survey data collected in parallel to the household budget survey and (b) CPI raw price data. The Engel approach requires no price data.

## _Price index approach_

We first calculate several bilateral price indexes, such as the Paasche index (Equation 1), Laspeyres index (Equation 2), and Fisher index (Equation 3), as described in Section 2.1, and compare the spatial price patterns indicated based on each approach. We also compare these results with those based on a multilateral price index (GEKS-Fisher index in Equation 8) to assess how transitivity (or lack thereof) influences the results.

## _CPD approach_

We examine the two types of CPD methods. The first approach is to use the weighted CPD (Equation 12) to calculate the multilateral price index by applying it to the item-level price data for which budget share information is available as the weight. While we apply both variable weights (Equation 13) and fixed weights (Equation 14), following Gibson, Le, and Kim (2017), we report only the results based on variable weights, as no substantial difference is found in the results depending on the weights.<sup>21</sup> The result of this approach is compared with a multilateral price index calculated by a GEKS-Fisher index method. Of particular interest in this comparison is how handling missing values by the CPD approach affects the spatial price measures.

## _Non-food prices_

As discussed in Section 2.2, the treatment of non-food items, particularly housing, is a vital issue in the calculation of spatial price indexes. The combination of using the CPD method and the CPI price data allows us to include many non-food items without losing quality information in the price data. In the approach, we compare the spatial patterns of (a) the food price index and (b) the food plus nonfood price index. In addition, we test the sensitivity of price measures to the omission of quality information (for both food and non-food items) by comparing the results with or without variety-level quality information in price observations.

For housing, we examine different approaches in the following aspects. First, we explore the influence of controlling for quality differences in housing across regions. We compare the results of spatial price measures based on the median values (that is, no control of quality) or hedonic regression (that is, with control of quality). Second, we also compare the results based on a price index that uses actually paid rents (that is, only rental units) and imputed rents (that is, owner-occupied and/or rent-free units included). The combination of these two aspects results in the following four housing approaches:

- _Median paid rent_ approach takes a median value of paid rents in each region.

- _Median imputed rent_ approach takes a median value of paid and imputed rents in each region.

- • _Hedonic paid rent_ approach estimates a hedonic regression model on paid rents in which coefficients for the regional dummy indicate housing price levels.

> 21 Results based on fixed weights are available upon request.

16