Inspired by the recent literature on aggregation theory, this paper introduces HITS, a semiparametric model of consumer demand that allows for diversity in tastes. The strong variation of budget shares observed across income groups has two possible origins: the individual income effect, and taste differences between poor and rich households. Consumer surveys reporting repeated cross sections do not permit the direct measurement of these two effects. In HITS, linear heterogeneity allows the GMM estimation of structural coefficients on an aggregate series. The joint density of spending and tastes is then recovered from cross sections by a nonparametric procedure involving a deconvolution. We estimate the model on British data (1968–1998) and report that taste heterogeneity explains a large fraction of the variation of budget shares with income.

This paper investigates the multifractal model of asset returns (MMAR), a class of continuous-time processes that incorporate the thick tails and volatility persistence exhibited by many financial time series. The simplest version of the MMAR compounds a Brownian motion with a multifractal time-deformation. Prices follow a semi-martingale, which precludes arbitrage in a standard two-asset economy. Volatility has long memory, and the highest finite moments of returns can take any value greater than 2. The local variability of a sample path is highly heterogeneous and is usefully characterized by the local Hölder exponent at every instant. In contrast with earlier processes, this exponent takes a continuum of values in any time interval. The MMAR predicts that the moments of returns vary as a power law of the time horizon. We confirm this property for Deutsche mark/U.S. dollar exchange rates and several equity series. We develop an estimation procedure and infer a parsimonious generating mechanism for the exchange rate. In Monte Carlo simulations, the estimated multifractal process replicates the scaling properties of the data and compares favorably with some alternative specifications.