The last two terms in equation (2) represent the second-order behavioral responses of the household. They include the effect of the price change on the quantities produced, delta q, and the quantities consumed, delta c, of each good j. Note that when prices fall due to trade liberalization the quantity produced could decline, thus reducing welfare for a given price, unless the household’s income shifts to other activities that can compensate the decline in income due to the fall of the price of good j. Similarly, consumption could increase as prices fall. Here, it is important not to get confused: if we only do the exercise with one single good j, we would erroneously conclude that welfare would fall as a consequence of the rise of consumption of the cheaper (liberalized) good. The key is to remember the summation sign: consumption of other goods would fall as the liberalized good would have become relatively cheaper. This clarification, however, brings us to the empirical estimations of the framework.

An important feature of this approach, which is consistent with the definition of IG, is that it emphasizes households’ abilities to change income sources and consumption patterns in response to changes in relative prices. With ideal data on household consumption and income patterns over time, combined with data on goods’ prices, it is possible to estimate the behavioral functions. Most countries, however, do not have the ideal panel data set. Instead, it is more common to have cross sections of households in living standards surveys. Table 1 lists 119 countries with surveys since 2000 with this type of data that are available from the World Bank’s Development Data Platform (DDP).<sup>5</sup>

# **B. Estimation Challenges**

Several estimation challenges emerge when attempting to estimate income-source and consumption responses to trade-driven price changes. One concerns price data. In practice, the relevant surveys ask households to report total expenditures by type of good or service, and they are also asked to report the number of units purchased. Analysts can then use these variables to compute unit values, the ratio of expenditures over the number of units. But unit values are not equal to prices for two main reasons. First, unless households maintain detailed records, self-reported expenditures and quantities are likely to suffer from measurement errors. Second, each category of goods or services probably contains many varieties, which might differ in terms of quality. Hence unit values, even if they were perfectly reported by the households, might reflect quality differences that vary systematically across types of households, and it is common to find positive partial correlations between expenditures and unit values in cross sectional estimations (see Deaton 1997; Lederman, Lichand and Fajnzylber 2011).

Fortunately, the literature has developed econometric estimations methods to deal with the measurement errors and the quality-valuation challenges discussed above. A full discussion of these approaches goes well beyond the scope of this short note. However, a bit of intuition might help busy operational staff and policymakers to think about the economics underlying the estimation challenges. An approach developed by Deaton (see Deaton 1988 and references in Deaton 1997) is to estimate a system of three equations: one for the determinants of unit values without location fixed effects, one for expenditures and one for income, both with location fixed effects (added by Porto 2005). The errors from those estimations can be used to correct for measurement errors and quality valuation, because

> 5 World Bank staff has online access to these surveys via DDP.

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