The paper considers the estimation of welfare measures when the functional form of demand is unknown. An adaptation of an argument of Gallant (1987) is used to show that welfare estimators based on a Fourier functional form for demand will be consistent under weak assumptions. Simulation evidence is presented for equivalent variation. True demand is a generalized Box–Cox function, estimated demand is a Fourier form, and equivalent variation is estimated by applying Vartia's (1983) algorithm to the estimated demand function. The estimator of equivalent variation has small asymptotic bias in the case of the assumed family of data generating processes.

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