We provide a method to estimate resource shares—the fraction of total household expenditure allocated to each household member—using linear (e.g., ordinary least squares) estimation of Engel curves. The method is a linear reframing of the 2013 nonlinear model of Dunbar, Lewbel, and Pendakur, extended to allow single-parent and other complex households, scale economies in assignable goods, and complementarities between nonassignable goods and supplemented with a linear identification test. We apply the model to data from 12 countries and investigate resource shares, gender gaps, and poverty at the individual level. We reject equal sharing and find large gender gaps in resource shares, and consequently in poverty rates, in some countries.

What is the role of transport improvements in globalization? We argue that the nineteenth century is the ideal testing ground for this question: freight rates fell on average by 50% while global trade increased 400% from 1870 to 1913. We estimate the first indices of bilateral freight rates for the period and directly incorporate these into a standard gravity model. We also take the endogeneity of bilateral trade and freight rates seriously and propose an instrumental variables approach. The results are striking as we find no evidence that the maritime transport revolution was the primary driver of the late nineteenth century global trade boom. Rather, the most powerful forces driving the boom were those of income growth and convergence.

We invent Implicit Marshallian demands, which combine desirable features of Hicksian and Marshallian demands. We propose and estimate the Exact Affine Stone Index (EASI) implicit Marshallian demand system. Like the Almost Ideal Demand (AID) system, EASI budget shares are linear in parameters given real expenditures. However, unlike the AID, EASI demands can have any rank and its Engel curves can have any shape over real expenditures. EASI error terms equal random utility parameters to account for unobserved preference heterogeneity. EASI demand functions can be estimated using GMM or three stage least squares, and, like AID, an approximate EASI model can be estimated by linear regression. (JEL D11, D12)

We prove a new identification theorem showing nonparametric identification of the joint distribution of random coefficients in general nonlinear and additive models. This differs from existing random coefficients models by not imposing a linear index structure for the regressors. We then model unobserved preference heterogeneity in consumer demand as utility functions with random Barten scales. These Barten scales appear as random coefficients in nonlinear demand equations. Using Canadian data, we compare estimated energy demand functions with and without random Barten scales. We find that unobserved preference heterogeneity substantially affects the estimated consumer surplus costs of an energy tax.

The share of household resources devoted to children is hard to identify because consumption is measured at the household level and goods can be shared. Using semiparametric restrictions on individual preferences within a collective model, we identify how total household resources are divided up among household members by observing how each family member's expenditures on a single private good like clothing vary with income and family size. Using data from Malawi we show how resources devoted to wives and children vary by family size and structure, and we find that standard poverty indices understate the incidence of child poverty. (JEL I31, I32, J12, J13, O12, O15)