_ESTIMATING FOOD PRICE INFLATION_ _3_ in subnational price survey systems. However, the capacity to monitor inflation continues to be severely limited by challenges related to data gathering that include such issues as lack of resources, loss of access to markets, or disturbances in ground operations during crises and conflict outbreaks. Despite tremendous effort, missing data remains pervasive, which poses problems when one wants to compute real-time inflation measured over multiple price series. Whenever a single price point is absent, the required index cannot be computed without making assumptions about missing data.

To overcome some of the shortcomings associated with traditional systems, this paper develops an approach for real-time imputation of survey data drawing on multiple imputation and ensemble learning ideas. The imputation is generated as an ensemble prediction from multiple completed price trajectories. Each price trajectory is the result of a stochastic equation chain of machine learning models that leverage correlations between prices of individual food items and similarities between markets to predict missing local price quotes. The idea is similar to a bootstrap aggregation (bag) of base learners (Breiman, 1996), only now randomization in base learners is not achieved by random sampling but from a stochastic simulation of chained model predictions. By augmenting incomplete and intermittent survey data with reliable predictions, subnational food price trends can be monitored continuously.

The paper highlights the new price monitoring capabilities using surveys from the World Food Programme (WFP) gathered in 25 fragile and conflict-affected countries. The final estimates of food price inflation documented in this paper are shown to capture important local inflation events related to conflict; as well as known food crises including the World Food Price Crisis of 2007-08 documented by Baffes et al. (2008); Concei ̧c ̃ao and Mendoza (2009), and the surge in inflation that followed the 2020 pandemic and subsequent expansion in the global monetary base. The results include inflation estimates for a large number of countries where these data have recently not been available, and the analysis of the results documents new insights into different characteristics of recent and past inflation events.

The granular high-frequency results provide an alternative price estimate that is particularly relevant in data-poor, lower-income, regions, where the capacity to maintain in-depth price monitoring programs, that rely on traditional CPI methods, is often limited. The focus on low-income countries is in contrast with past work that, instead, has had a stronger focus on data-rich and higher income areas. For example, past related work has developed forecasting methods for future CPI (Joutz, 1997; Gavin and Mandal, 2002), future commodity spot and futures prices at global markets (Ahumada and Cornejo, 2016; Ouyang et al., 2019), or methods for continuously updating current expectations of future country-level CPI inflation using information from alternative sources (Modugno, 2011; Seabold and Coppola, 2015). Finally, the methods proposed by the paper could also be applied to enhance other data gathering programs, improve their cost-effectiveness