Multilevel Models Vs. Fixed Regression, Insights from Food Prices and Consumption in Mexico
Changes in prices as well as in socioeconomic population composition could affect household consumption. Teasing apart period and cohort effects are central to understand how household welfare responds to changing contextual conditions, and to design better mitigation policies. In this paper, we compare multilevel models and fixed effects models to understand the impact of prices on food expenditures in Mexico. The latter methodology has been the most common tool in policy assessment, but recent studies have drawn attention to their capacity for assessing period effects.
We pooled 14 cross-sectional data of the National Survey of Income and Expenditure (1984-2012) and constructed a pseudo-panel that allows considering cohorts and periods. We first estimate fixed-effect models we construct a pseudo-panel based on birth cohorts, place of residence and household production characteristics. Then, we use a two-way pseudo-panel model to account for period and cohort effects. By using fixed effects, we simultaneously accommodate for the influence of observed and unobserved attributes on food consumption across multiple time points. Second, we adjust a cross-classified multilevel model where households are nested, simultaneously in period (survey year) and birth cohort. By adjusting random effects, we can describe household-level relationships that might vary over time, and over cohorts. We introduce food prices as period predictors while controlling for sociodemographic characteristics and cohort membership. We compare the results to address the following questions: a) how are price changes treated in the two approaches; b) how they differ on accounting for population change over time; and c) how they account for unobservables and how that could affect their conclusion for causal analysis.