Aggregation of Non Stationary Demand Systems

This paper studies under which conditions a cross-sectional regression yields unbiased estimates of the parameters of an individual dynamic model with fixed effects and individual-specific responses to macro shocks. We show that the OLS estimation of a relationship involving non stationary variables on a cross-section yields estimates which converge to the true value when calendar time tends to infinity. We then consider the particular case of an AI demand model, and we show, using French quarterly aggregate time-series, that budget shares, relative prices and the log of real total expenditure are I(1) and form a cointegrated system. We compare these macro estimates to estimates obtained from three Family Expenditure Surveys and find large differences.