where Δ _w_ is the welfare effect expressed in percentage terms of the baseline income or consumption level of household _i_ , Δ _p_ is the percentage change in food prices (this can be estimated for one or more food consumption items), _PR_ is the food production ratio (at the aggregate level for a household, this can be proxied by the household’s agricultural sales divided by its total income or consumption, but it is also feasible to analyze this variable for various food items one by one), _CR_ is the food expenditure ratio (which at the aggregate household level is captured by the household’s food consumption divided its total income or consumption, but again this can also be examined for each specific food item separately), and finally η is the wage rate elasticity with respect to food price changes and _L_ is the labor share in total household income or consumption.

The interpretation of the above equation is straightforward. If a household is a net seller of food (in the aggregate or for any specific food item) _PR_ will be larger than _CR_ and the household will benefit from the price increase. By contrast, if the household is a net purchaser of food, the first term in the above equation will be negative. As to the second term, it captures the potential compensating effect of higher wages, for example for those households who have some of their members providing wage labor in foodproducing farms. While the framework is very simple, there are a number of implicit assumptions embedded in it that we will need to carefully consider. There may also be issues with estimating the variables in that equation. For example, depending on data availability we can estimate the wage elasticity directly or use a range of plausible estimates from other work and carry out sensitivity analysis. In the absence of good estimates of these wage elasticities (especially in sub-Saharan Africa), researchers may also decide to compute short- term effects by not including the potential gains through wages. Following Deaton’s methodology, beyond statistical point estimates of the impact of higher food prices, one may also estimate non-parametric kernel regressions by location, by net market position, by occupation etc.

The distinction between the short and long run impact of price rises is also important. Ravallion (1990 and 2000) uses data from Bangladesh and India to argue that while in the short run the rural poor are adversely affected when the relative price of food rises, the impact in the long run can be neutral after adjusting for changes in wage rates. This result is due to the increased price elasticity of the wage rate to the price of foodgrains in the long run. However, the extent to which wages do in fact respond to changes in food prices has been called into question by Rashid (2002). Using time series data the author argues that since the mid- eighties changes in rice prices have had a negligible impact on agricultural wages in Bangladesh. Using data from a number of African countries, Christaensen and Demery (2006) extend this analysis of second-round effects by including an additional effect of increased farm productivity arising from the increase in price of food staples. Their main conclusion is that policies leading to higher food prices are likely to increase poverty, even after factoring in countervailing wage and productivity effects.